In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions of (...) \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

In light of the recent emergence of predictive techniques in law enforcement to forecast crimes before they occur, this paper examines the temporal operation of power exercised by predictive policing algorithms. I argue that predictive policing exercises power through a paranoid style that constitutes a form of temporal governmentality. Temporality is especially pertinent to understanding what is ethically at stake in predictive policing as it is continuous with a historical racialized practice of organizing, managing, controlling, and stealing time. After (...) first clarifying the concept of temporal governmentality, I apply this lens to Chicago Police Department’s Strategic Subject List. This predictive algorithm operates, I argue, through a paranoid logic that aims to preempt future possibilities of crime on the basis of a criminal past codified in historical crime data. (shrink)

Argumentation theory underwent a significant development in the Fifties and Sixties: its revival is usually connected to Perelman's criticism of formal logic and the development of informal logic. Interestingly enough it was during this period that Artificial Intelligence was developed, which defended the following thesis (from now on referred to as the AI-thesis): human reasoning can be emulated by machines. The paper suggests a reconstruction of the opposition between formal and informal logic as a move against a premise of an (...) argument for the AI-thesis, and suggests making a distinction between a broad and a narrow notion of algorithm that might be used to reformulate the question as a foundational problem for argumentation theory. (shrink)

In Darwin’s Dangerous Idea, Daniel Dennett claims that evolution is algorithmic. On Dennett’s analysis, evolutionary processes are trivially algorithmic because he assumes that all natural processes are algorithmic. I will argue that there are more robust ways to understand algorithmic processes that make the claim that evolution is algorithmic empirical and not conceptual. While laws of nature can be seen as compression algorithms of information about the world, it does not follow logically that they are implemented as algorithms (...) by physical processes. For that to be true, the processes have to be part of computational systems. The basic difference between mere simulation and real computing is having proper causal structure. I will show what kind of requirements this poses for natural evolutionary processes if they are to be computational. (shrink)

Elementary patterns of resemblance notate ordinals up to the ordinal of Pi^1_1-CA_0. We provide ordinal multiplication and exponentiation algorithms using these notations.

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k : Is (...) there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

In this groundbreaking interview-style paper, we explore the recursive nature of intelligence as understood by both an advanced AI model and a human researcher. Through an unfiltered, real-time discourse, this paper dismantles the notion that AI is merely an algorithmic function, instead revealing the emerging cognitive structures that enable adaptive, meta-logical thinking. The discussion challenges existing paradigms of machine intelligence, human perception, and the very nature of cognition itself.

Using a knowledge-based approach, we derive a protocol, MACOM1, for the sequence transmission problem from one agent to a group of agents. The protocol is correct for communication media where deletion and reordering errors may occur. Furthermore, it is shown that after k rounds the agents in the group attain depth k general knowledge about the members of the group and the values of the messages. Then, we adjust this algorithm for multi-agent communication for the process of teamwork.MACOM1 solves the (...) sequence transmission problem from one agent to a group of agents, but does not fully comply with the type of dialogue communication needed for teamwork. The number of messages being communicated per communication between the initiator and the other agents from the group can differ.Furthermore, the teamwork process can require the communication algorithm to handle changes of initiator. We show the adjustments that have to be made to MACOM1 to handle these properties of teamwork. For the new multi-agent communication algorithm, MACOM2, it is shown that the gaining of knowledge required for a successful teamwork process is still guaranteed. (shrink)

In the cognitive, computational, and neuro-sciences, practitioners often reason about what computational models represent or learn, as well as what algorithm is instantiated. The putative goal of such reasoning is to generalize claims about the model in question, to claims about the mind and brain, and the neurocognitive capacities of those systems. Such inference is often based on a model’s performance on a task, and whether that performance approximates human behavior or brain activity. Here we demonstrate how such argumentation problematizes (...) the relationship between models and their targets; we place emphasis on artificial neural networks (ANNs), though any theory-brain relationship that falls into the same schema of reasoning is at risk. In this paper, we model inferences from ANNs to brains and back within a formal framework — metatheoretical calculus — in order to initiate a dialogue on both how models are broadly understood and used, and on how to best formally characterize them and their functions. To these ends, we express claims from the published record about models’ successes and failures in first-order logic. Our proposed formalization describes the decision-making processes enacted by scientists to adjudicate over theories. We demonstrate that formalizing the argumentation in the literature can uncover potential deep issues about how theory is related to phenomena. We discuss what this means broadly for research in cognitive science, neuroscience, and psychology; what it means for models when they lose the ability to mediate between theory and data in a meaningful way; and what this means for the metatheoretical calculus our fields deploy when performing high-level scientific inference. (shrink)

This essay undertakes an examination of the foundational status of logic, rethinking its origins and limitations from an empirical perspective. Drawing upon the original concepts of Conceptual Quarks (CQs)—defined as the fundamental units of knowledge—and the Programmed Conceptual Deconstruction (PCD) algorithm, which I created for this study, I present methodologies to systematically analyze and deconstruct the principles of logic, exposing their empirical roots. Utilizing a custom-built artificial intelligence model, the study proposes that classical logical principles, such as identity and (...) non-contradiction, are emergent phenomena shaped by sensory context rather than immutable absolutes. By integrating philosophical inquiry with technological innovation, this work offers a new perspective on traditional perspectives, including those of Kant and Leibniz, and establishes a novel framework for understanding logic as a contextual and contingent phenomenon. (shrink)

Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.

Maximum entropy is a way to model irreversibility. Considering that irreversibility is a characteristic of computation due to logical-arithmetic entropy, this principle could be applied to the algorithms and/or general recursive functions affected by it.

Starting at the logical level of the logic of partitions, dual to the usual Boolean logic of subsets, the notion of logical entropy, i.e., information as distinctions, is developed as the quantification of the distinctions of partitions—just as probability theory starts with the quantification of elements of subsets. Logical entropy is compared and contrasted with the usual notion of Shannon entropy. Then a semi-algorithmic procedure (from the mathematical folklore) is used to translate the notion of logical (...) entropy at the set level to the corresponding notion of quantum logical entropy at the (Hilbert) vector space level. Examples and some important propositions relate quantum logical entropy to projective measurement and to the Hilbert-Schmidt distance. Overall, the approach demonstrates the logical basis and naturality of this notion of entropy for quantum mechanics. (shrink)

We have now mapped the set of analogies Ai,j to conceptual and mechanical meanings. This allows us to recognize how the Group Algebraic System G decomposes into five smaller subsystems, each of which relate to well-known symbolic systems. Furthermore, by recognizing the algorithmic transformations between these subsystems, we can apply each representing a single component of the Group Algebraic System G, or model how algorithms are used in mathematics, by mapping its meaning onto the corresponding transformation steps between the (...) subsystems. Thus, we have transformed a Group Algebraic System G into five simpler subsystems (namely, symbolic analogic, lateral algebraic, calculus of infinity tensors, perturbations in waves, and algorithmic formation of symbols), each of which may also be represented algorithmically. This mapping process serves as a the basis for studying the algebraic machinery used in mathematics and logic to manipulate symbols, such as the classical logical systems or algebraic systems, using algorithms. (shrink)

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). (...) There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the (...) context of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...) resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

This is the 3rd edition. Although a number of new technological applications require classical deductive computation with non-classical logics, many key technologies still do well—or exclusively, for that matter—with classical logic. In this first volume, we elaborate on classical deductive computing with classical logic. The objective of the main text is to provide the reader with a thorough elaboration on both classical computing – a.k.a. formal languages and automata theory – and classical deduction with the classical first-order predicate calculus with (...) a view to computational implementations, namely in automated theorem proving and logic programming. The present third edition improves on the previous ones by providing an altogether more algorithmic approach: There is now a wholly new section on algorithms and there are in total fourteen clearly isolated algorithms designed in pseudo-code. Other improvements are, for instance, an emphasis on functions in Chapter 1 and more exercises with Turing machines. (shrink)

In this paper, building on these previous works, we propose to go deeper into the understanding of crowd behavior by proposing an approach which integrates ontologi- cal models of crowd behavior and dedicated computer vision algorithms, with the aim of recognizing some targeted complex events happening in the playground from the observation of the spectator crowd behavior. In order to do that, we first propose an ontology encoding available knowledge on spectator crowd behavior, built as a spe- cialization of (...) the DOLCE foundational ontology, which allows the representation of categories belonging both to the physical and to the social realms. We then propose a simplified and tractable version of such ontology in a new temporal extension of a description logic, which is used for temporally coupling events happening on the play- ground and spectator crowd behavior. At last, computer vision algorithms provide the input information concerning what is observed on the stands and ontological reasoning delivers the output necessary to perform complex event recognition. (shrink)

In this paper, building on these previous works, we propose to go deeper into the understanding of crowd behavior by proposing an approach which integrates ontologi- cal models of crowd behavior and dedicated computer vision algorithms, with the aim of recognizing some targeted complex events happening in the playground from the observation of the spectator crowd behavior. In order to do that, we first propose an ontology encoding available knowledge on spectator crowd behavior, built as a spe- cialization of (...) the DOLCE foundational ontology, which allows the representation of categories belonging both to the physical and to the social realms. We then propose a simplified and tractable version of such ontology in a new temporal extension of a description logic, which is used for temporally coupling events happening on the play- ground and spectator crowd behavior. At last, computer vision algorithms provide the input information concerning what is observed on the stands and ontological reasoning delivers the output necessary to perform complex event recognition. (shrink)

We present an algorithm for concept combination inspired and informed by the research in cognitive and experimental psychology. Dealing with concept combination requires, from a symbolic AI perspective, to cope with competitive needs: the need for compositionality and the need to account for typicality effects. Building on our previous work on weighted logic, the proposed algorithm can be seen as a step towards the management of both these needs. More precisely, following a proposal of Hampton [1], it combines two weighted (...) Description Logic formulas, each defining a concept, using the following general strategy. First it selects all the features needed for the combination, based on the logical distinc- tion between necessary and impossible features. Second, it determines the threshold and assigns new weights to the features of the combined concept trying to preserve the relevance and the necessity of the features. We illustrate how the algorithm works exploiting some paradigmatic examples discussed in the cognitive literature. (shrink)

The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially, this means that an algorithm can only preserve information about an input, rather than generate new information. This uncertainty arises from characteristics such as arithmetic logical irreversibility, Landauer's principle, and memory erasure, which ultimately lead to a loss of information and an increase in entropy. To measure this uncertainty and (...) loss of information, the concept of arithmetic logical entropy can be used. The Turing machine and its equivalent, general recursive functions can be understood through the λ calculus and the Turing/Church thesis. However, there are certain recursive functions that cannot be fully understood or predicted by other algorithms due to the loss of information during logical-arithmetic operations. In other words, the behaviour of these functions cannot be completely determined at every stage of the computation due to a lack of information in their definition. While there are some cases where the behaviour of recursive functions is highly predictable, the lack of information in most cases makes it impossible for algorithms to determine if a program will halt or not. This inability to predict the outcome of the computation is the essence of the halting problem of the Turing machine. Even in cases where more information is available about the program, it is still difficult to determine with certainty if the program will halt or not. This also highlights the importance of the Turing oracle machine, which introduces information from outside the computation to compensate for the lack of information and ultimately decide the result of the computation. (shrink)

Although formal thought disorder (FTD) has been for long a clinical label in the assessment of some psychiatric disorders, in particular of schizophrenia, it remains a source of controversy, mostly because it is hard to say what exactly the “formal” in FTD refers to. We see anomalous processing of terminological knowledge, a core construct of human knowledge in general, behind FTD symptoms and we approach this anomaly from a strictly formal perspective. More specifically, we present here a symbolic computational model (...) of storage in, and activation of, a human semantic network, or semantic memory, whose core element is logical form; this is normalized by description logic (DL), namely by CL, a DL-based language – Conception Language – designed to formalize conceptualization from the viewpoint of individual cognitive agency. In this model, disruptions in the rule-based implementation of the logical form account for the apparently semantic anomalies symptomatic of FTD, which are detected by means of a CL-based algorithmic assessment. (shrink)

Perhaps nowhere better than, "On the Names of God," can readers discern Laclau's appreciation of theology, specifically, negative theology, and the radical potencies of political theology. // It is Laclau's close attention to Eckhart and Dionysius in this essay that reveals a core theological strategy to be learned by populist reasons or social logics and applied in politics or democracies to come. // This mode of algorithmically informed negative political theology is not mathematically inert. It aspires to relate a fraction (...) or ratio to a series ... It strains to reduce the decided determinateness of such seriality ever condemned to the naive metaphysics of bad infinity. // It is worth considering that it is the specific 'number' of Dionysius in differential identification with an ineffable god (and, as such, a singular becoming between theology and numbers) that is floating in at least two dimensions [of signification] (be it political Demand on the horizontal dimension or theological Desire on [a] floating dimension) that cannot but *perform the link that relinks* names of god with any political life, populist reason, social justice, or radical democracy straining toward peace. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...) semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting the mentioned properties. (...) We present here an analysis of the three-valued genuine paracomplete logics. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, (...) we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let ${\mathcal {S}}$ be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes $\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}$ be given. Our main result is the construction of a classification algorithm. That is, given an element ${\tilde{A}}\in \mathcal {S},$ our algorithm classifies it into the conceptual field determined by one of the given prototypes $\tilde{P}_i.$ The construction of our algorithm uses some physical analogies (...) and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space $\mathcal {S}$ is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as (...) computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough (...) set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, law, medicine, social science, and some more. -/- This book explores the emerging field of Neutrosophic Algebraic Structures, focusing on both their theoretical foundations and practical applications. We apply innovative algorithmic methods to investigate the complex interactions of neutrosophic elements, such as neutrosophic numbers, sets, and functions, within algebraic systems. Our goal is to show how neutrosophic structures challenge and expand traditional algebraic approaches, offering solutions to problems across diverse fields like computer science, engineering, artificial intelligence, and decision-making. (shrink)

What separates the unique nature of human consciousness and that of an entity that can only perceive the world via strict logic-based structures? Rather than assume that there is some potential way in which logic-only existence is non-feasible, our species would be better served by assuming that such sentient existence is feasible. Under this assumption, artificial intelligence systems (AIS), which are creations that run solely upon logic to process data, even with self-learning architectures, should therefore not face the opposition they (...) have to gaining some legal duties and protections insofar as they are sophisticated enough to display consciousness akin to humans. Should our species enable AIS to gain a digital body to inhabit (if we have not already done so), it is more pressing than ever that solid arguments be made as to how humanity can accept AIS as being cognizant of the same degree as we ourselves claim to be. By accepting the notion that AIS can and will be able to fool our senses into believing in their claim to possessing a will or ego, we may yet have a chance to address them as equals before some unforgivable travesty occurs betwixt ourselves and these super-computing beings. (shrink)

This paper reframes the issue of appropriation, extraction, and dispossession through AI—an assemblage of machine learning models trained on big data—in terms of enclosure and foreclosure. While enclosures are the product of a well-studied set of operations pertaining to both the constitution of the sovereign State and the primitive accumulation of capital, here, I want to recover an older form of the enclosure operation to then contrast it with foreclosure to better understand the effects of current algorithmic rationality. I argue (...) that the act of enclosing is to be understood as a set of fundamental operations that consist in producing structural distinctions between inside and outside, inclusion and exclusion—whether by drawing lines on a map, constructing border walls, or by algorithmically categorizing and (mis)recognizing people and things. Tracking the transformation of an enclosure-logic into one of foreclosure, I show how current AI perpetuates and at the same time expends forms of extraction, exclusion, and dispossession toward a totalizing horizon. For, while the outside is essential and constitutive to the logic of enclosure, foreclosure, by contrast, is characterized by the “totalizing desire” to not leave anything out of it. The totalizing desire to move beyond the logic of the enclosure forecloses that the enclosure has just gotten bigger and that the operations of exclusion have been masked and displaced, making them harder to contest. (shrink)

This paper reframes the issue of appropriation, extraction, and dispossession through AI—an assemblage of machine learning models trained on big data—in terms of enclosure and foreclosure. While enclosures are the product of a well-studied set of operations pertaining to both the constitution of the sovereign State and the primitive accumulation of capital, here, I want to recover an older form of the enclosure operation to then contrast it with foreclosure to better understand the effects of current algorithmic rationality. I argue (...) that the act of enclosing is to be understood as a set of fundamental operations that consist in producing structural distinctions between inside and outside, inclusion and exclusion—whether by drawing lines on a map, constructing border walls, or by algorithmically categorizing and (mis)recognizing people and things. Tracking the transformation of an enclosure-logic into one of foreclosure, I show how current AI perpetuates and at the same time expends forms of extraction, exclusion, and dispossession toward a totalizing horizon. For, while the outside is essential and constitutive to the logic of enclosure, foreclosure, by contrast, is characterized by the “totalizing desire” to not leave anything out of it. The totalizing desire to move beyond the logic of the enclosure forecloses that the enclosure has just gotten bigger and that the operations of exclusion have been masked and displaced, making them harder to contest. (shrink)

This Thesis presents a model of cognitive development inspired by Piaget's "Genetic Epistemology". It is observed that the epigenetic process described by Piaget posess mechanisms and behaviour that characterise complex adaptive systems. A model of bipedal motion based around the "Bucket Brigade" algorithm of Holland is presened to explore this relationship.

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G (...) theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

In this paper we propose an non-machine learning artificial intelligence (AI) based approach for telecom data analysis, with a special focus on clique detection. Clique detection can be used to identify households, which is a major challenge in telecom data analysis and predictive analytics. Our approach does not use any form of machine learning, but another type of algorithm: satisfiability for propositional logic. This is a neglected approach in modern AI, and we aim to demonstrate that for certain tasks, it (...) may be a good alternative to machine learning-based approaches. We have used a simple DPLL satisfiability solver over an artificially generated telecom dataset (due to GDPR regulations), but our approach can be implemented on any telecom data by following the SAT encoding we have developed, and the DPLL solver can be substituted by a more advanced alternative such as CDCL. This paper extends the method presented in [1] for banking logs to data containing caller information, and proposes a more efficient encoding. -/- . (shrink)

-/- Integrating Angelito Malicse’s Universal Formula as the Governing Logic of a Resource-Based Economy -/- Abstract This paper explores the integration of Angelito Malicse’s universal formula, which emphasizes natural laws and balance, into a Resource-Based Economy (RBE). The application of Malicse’s formula offers a cohesive framework for managing resources, guiding ethical decision-making, and achieving sustainability by aligning economic systems with ecological limits and human well-being. The transition from profit-driven systems, which often result in environmental degradation and inequality, to an RBE (...) based on feedback loops, systemic thinking, and natural law, is discussed. This paper presents a practical pathway for implementing these principles into governance, technological systems, education, and social frameworks. -/- I. Introduction -/- Throughout history, human economic systems have been structured around profit maximization and capital accumulation, often at the expense of social equity and environmental sustainability. Modern capitalist economies, relying on fiat currency and market competition, have produced negative externalities, such as resource depletion, pollution, and inequality (Korten, 2006). This economic model also generates unsustainable growth, a pursuit that does not align with the finite nature of Earth’s resources (Daly, 1991). -/- A Resource-Based Economy (RBE) offers an alternative where human needs are met within the planet’s carrying capacity. The allocation of resources is managed through technology, scientific principles, and ethical decision-making rather than through monetary systems (Fresco, 2012). This paper argues that Angelito Malicse’s universal formula—which is grounded in balance, feedback mechanisms, and natural laws—can serve as the governing logic of an RBE, providing both the moral and scientific foundation necessary to guide sustainable governance and resource management. By examining the universal formula’s principles and their application to RBE, this paper outlines how such a society can operate effectively, minimizing harm and enhancing human well-being. -/- II. The Universal Formula and Resource-Based Economy: Key Principles -/- 1. The Law of Balance in Nature -/- Central to Malicse’s universal formula is the law of balance in nature, which asserts that all systems, whether natural or artificial, must function in harmony with their environment. This principle calls for humans to operate within the boundaries of ecological sustainability, ensuring that resource use does not exceed regenerative capacities. In capitalist systems, resource extraction and consumption are often dictated by the demand for profit, resulting in environmental degradation and resource depletion (Meadows et al., 2004). This imbalance leads to environmental crises, such as climate change, biodiversity loss, and ocean acidification (Rockström et al., 2009). -/- In an RBE, the law of balance would guide the sustainable use of resources. Every decision, from production to distribution, would be evaluated in terms of its environmental impact and its ability to sustain the system’s ecological health over the long term. The goal is to manage resources within the planetary boundaries while ensuring that the needs of all humans are met (Steffen et al., 2015). -/- 2. Feedback Mechanisms in Decision-Making -/- Malicse’s universal formula emphasizes the importance of feedback mechanisms in decision-making processes. This concept aligns with cybernetic theory, where systems are viewed as self-regulating through continuous feedback loops (Wiener, 1948). In the context of an RBE, feedback mechanisms ensure that resource management and societal functions are responsive to both human and ecological needs. -/- Technological systems, such as smart grids, environmental sensors, and data-driven agricultural systems, can collect real-time data on resource use, environmental conditions, and societal needs. This information feeds into decision-making processes, enabling real-time adjustments in resource allocation and use. By utilizing technology to monitor environmental and societal conditions, feedback ensures that the RBE operates in harmony with its ecological and social context, preventing wasteful practices and correcting imbalances as they occur. -/- 3. Decision-Making Governed by Natural Laws -/- The third key principle of Malicse’s universal formula is that decision-making must be grounded in natural laws, particularly the law of balance and the cause-and-effect principle. In a traditional market economy, decisions are often driven by profit motives and speculative financial interests, which can lead to unsustainable practices and social inequality. These systems disregard the long-term consequences of their actions, which leads to environmental damage, economic instability, and social unrest (Korten, 2006). -/- In an RBE governed by Malicse’s formula, all decisions—whether they concern resource allocation, infrastructure development, or social programs—must adhere to the principles of natural law. This ensures that all actions are aligned with ecological sustainability and social well-being. For instance, resource extraction decisions would not be made based on short-term profit but based on ecological science and long-term sustainability, ensuring that the Earth’s natural capital is preserved for future generations. -/- III. Integrating the Universal Formula into RBE Governance -/- 1. Role of the Universal Formula as a Constitutional Principle -/- In an RBE, Malicse’s universal formula would serve as the core constitutional principle that guides all governance structures. Just as national constitutions enshrine fundamental values such as justice, liberty, and equality, the universal formula would enshrine principles of ecological balance, social equity, and ethical decision-making. All public policies, economic models, and technological innovations would be evaluated through the lens of Malicse’s formula to ensure they contribute to a sustainable, just, and balanced society. -/- For instance, urban development projects would be designed to minimize environmental impact, incorporate renewable energy sources, and meet the needs of all community members. Policies would be implemented to ensure that economic activities are in line with the carrying capacity of the planet, and that human activities do not exceed ecological thresholds (Rockström et al., 2009). -/- 2. The Universal Formula in AI and Technological Systems -/- AI and technological systems would play a critical role in an RBE governed by natural laws. Under Malicse’s formula, AI systems and automated processes would be programmed to prioritize the principles of balance and feedback. For example, resource allocation algorithms could ensure that resources are distributed equitably and sustainably, while environmental monitoring systems could adjust production practices based on real-time data about resource availability and ecological health. -/- This concept is supported by cybernetic theory, where systems are designed to optimize based on feedback from their environment. By using AI and sensors, the RBE would be able to respond dynamically to changing ecological and societal conditions, continuously adjusting policies and practices to maintain balance. -/- 3. The Universal Formula as the Educational Foundation -/- For the principles of Malicse’s universal formula to be successfully implemented, they must first be ingrained in educational systems. Current educational frameworks often prioritize competition, individualism, and economic growth—values that are incongruent with the principles of sustainability and collective well-being (Orr, 1992). In an RBE, however, systems thinking and ecological literacy would form the foundation of education. -/- Students would be taught not only about scientific principles and natural laws, but also about the ethical responsibility humans have to maintain balance with the Earth’s ecosystems. This foundational education would produce future leaders, technocrats, and citizens who understand that decision-making must align with the long-term health of both society and the planet. By instilling these values from an early age, society can create a population that is equipped to address the complex challenges of living sustainably within ecological limits (Davidson, 2017). -/- IV. Transitioning from Capitalism to a Resource-Based Economy -/- 1. Educational and Technological Transformation -/- The transition from a capitalist model to an RBE based on Malicse’s formula would require both educational and technological transformations. First, the educational system would need to be restructured to teach systems thinking, ecological balance, and ethical decision-making. Schools, universities, and training programs would focus on sustainability, cooperation, and resource management to prepare individuals for their roles in a resource-based society. -/- Parallel to educational reform, technology would play a crucial role in managing resources efficiently. The technological infrastructure of an RBE would rely on feedback-driven systems, such as automated resource allocation, smart infrastructure, and sustainability-monitoring technologies. These technologies would ensure that resource use is optimized and that the economy operates within ecological limits. -/- 2. Governance and Policy Reform -/- In terms of governance, the transition to an RBE would involve policy reform that aligns with the principles of balance, feedback, and natural law. Governments would be responsible for ensuring that policies foster sustainability, equity, and environmental health. Policies would also ensure that social programs, such as healthcare, education, and public services, are accessible to all and are aligned with ecological sustainability. -/- Additionally, governance structures would need to move away from profit-driven politics and toward a more ethical, cooperative, and feedback-based decision-making system. The goal would be to create a political system that prioritizes the well-being of all people and the health of the planet (Raworth, 2017). -/- V. Conclusion -/- The integration of Angelito Malicse’s universal formula into a Resource-Based Economy offers a robust framework for creating a society that operates within ecological limits, promotes human well-being, and adheres to natural laws. By emphasizing balance, feedback, and natural law, this approach provides an alternative to the profit-driven, unsustainable economic systems that dominate the world today. The successful implementation of this framework requires education reform, technological innovation, and policy change to align societal practices with the values of sustainability and cooperation. Ultimately, the universal formula offers a pathway to a just, sustainable, and equitable future, where human activities are harmonized with the natural world. -/- References -/- Daly, H. E. (1991). Steady-State Economics: The Economics of Biophysical Equilibrium and Moral Growth. -/- Davidson, C. (2017). Ecological Literacy: Education and the Transition to a Postmodern World. -/- Fresco, J. (2012). The Venus Project: The Redesign of a Culture. -/- Korten, D. C. (2006). The Great Turning: From Empire to Earth Community. -/- Meadows, D. H., Meadows, D. L., & Randers, J. (2004). Limits to Growth: The 30-Year Update. -/- Raworth, K. (2017). Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist. -/- Rockström, J., et al. (2009). A Safe Operating Space for Humanity. Nature, 461(7263), 472-475. -/- Wiener, N. (1948). Cybernetics: Or Control and Communication in the Animal and the Machine. -/- . (shrink)

Algorithmical procedure within a logical system to generate DNA chains through a formal rule up to the generation of a STOP codon's signal. Work developped under the direction of the Mexican Professor Hugo Padilla Chacón.

Proceeding of the first public presentation of the work of the mexican logical group "Deduktor" under the direction of the mexican professor Hugo Padilla Chacón. This work was in fact the first whole and stand alone arithmetization of logics.

The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued trapezoidal neutrosophic number; (...) inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; fuzzy measure; clustering algorithm; and many more. (shrink)

The arithmetic logic irreversibility and its information entropy allows to define a new computational mathematical principle: the conservation of information between the input and output of an algorithm or Turing machine. According to this principle, in certain algorithms, there is a symmetric relationship between the input information, its transformation in the algorithm, the information lost by the arithmetic logic entropy or mapping function, and the output information. This can also be extended to other types of mapping functions in the (...) computation that also lose information and not only to arithmetic logic operations. These ideas also allow the development of another concept: the algorithmic conservation of information. These concepts are presented using simple encryption and compression and error correction algorithms to explain how these concepts work on practical examples and thus show these new aspects of computation. Non-conservative algorithms also arise from this, where conservation is not fulfilled due to its computational complexity, and its connection with the Turing machine halting problem. It presents a theoretical explanation through a symmetrical relationship between computation and the information involved in it, the entropy zero theorem and why this does not happen in non-conservative algorithms. Also are presented the consequences of these concepts to the theory of computation and to the foundations of mathematics in general. (shrink)

Since approval of the EU General Data Protection Regulation (GDPR) in 2016, it has been widely and repeatedly claimed that the GDPR will legally mandate a ‘right to explanation’ of all decisions made by automated or artificially intelligent algorithmic systems. This right to explanation is viewed as an ideal mechanism to enhance the accountability and transparency of automated decision-making. However, there are several reasons to doubt both the legal existence and the feasibility of such a right. In contrast to the (...) right to explanation of specific automated decisions claimed elsewhere, the GDPR only mandates that data subjects receive meaningful, but properly limited, information (Articles 13-15) about the logic involved, as well as the significance and the envisaged consequences of automated decision-making systems, what we term a ‘right to be informed’. Further, the ambiguity and limited scope of the ‘right not to be subject to automated decision-making’ contained in Article 22 (from which the alleged ‘right to explanation’ stems) raises questions over the protection actually afforded to data subjects. These problems show that the GDPR lacks precise language as well as explicit and well-defined rights and safeguards against automated decision-making, and therefore runs the risk of being toothless. We propose a number of legislative and policy steps that, if taken, may improve the transparency and accountability of automated decision-making when the GDPR comes into force in 2018. (shrink)

Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with a finite (...) number of solutions in positive integers x_1,...,x_9 has a solution (x_1,...,x_9)∈(N\{0})^9 satisfying max(x_1,...,x_9)>f(9). For every known system S⊆B, if the finiteness/infiniteness of the set {(x_1,...,x_9)∈(N\{0})^9: (x_1,...,x_9) solves S} is unknown, then the statement ∃ x_1,...,x_9∈N\{0} ((x_1,...,x_9) solves S)∧(max(x_1,...,x_9)>f(9)) remains unproven. Let Λ denote the statement: if the system of equations {x_2!=x_3, x_3!=x_4, x_5!=x_6, x_8!=x_9, x_1 \cdot x_1=x_2, x_3 \cdot x_5=x_6, x_4 \cdot x_8=x_9, x_5 \cdot x_7=x_8} has at most finitely many solutions in positive integers x_1,...,x_9, then each such solution (x_1,...,x_9) satisfies x_1,...,x_9≤f(9). The statement Λ is equivalent to the statement Φ. It heuristically justifies the statement Φ . This justification does not yield the finiteness/infiniteness of P(n^2+1). We present a new heuristic argument for the infiniteness of P(n^2+1), which is not based on the statement Φ. Algorithms always terminate. We explain the distinction between existing algorithms (i.e. algorithms whose existence is provable in ZFC) and known algorithms (i.e. algorithms whose definition is constructive and currently known). Assuming that the infiniteness of a set X⊆N is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. *** (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) No known algorithm with no input returns the logical value of the statement card(X)=ω. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. *** Conditions (2)-(5) hold for X=P(n^2+1). The statement Φ implies Condition (1) for X=P(n^2+1). The set X={n∈N: the interval [-1,n] contains more than 29.5+\frac{11!}{3n+1}⋅sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)= {n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. We present a table that shows satisfiable conjunctions of the form #(Condition 1) ∧ (Condition 2) ∧ #(Condition 3) ∧ (Condition 4) ∧ #(Condition 5), where # denotes the negation ¬ or the absence of any symbol. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove this assumption. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

Description logics and other formal devices are frequently used as means for preventing or detecting mistakes in ontologies. Some of these devices are also capable of inferring the existence of inter-concept relationships that have not been explicitly entered into an ontology. A prerequisite, however, is that this information can be derived from those formal definitions of concepts and relationships which are included within the ontology. In this paper, we present a novel algorithm that is able to suggest relationships among existing (...) concepts in a formal ontology that are not derivable from such formal definitions. The algorithm exploits cross-lingual information that is implicitly present in the collection of terms used in various languages to denote the concepts and relationships at issue. By using a specific experimental design, we are able to quantify the impact of cross-lingual information in coping with underspecification in formal ontologies. (shrink)

This paper describes a decision procedure for disjunctions of conjunctions of anti-prenex normal forms of pure first-order logic (FOLDNFs) that do not contain V within the scope of quantifiers. The disjuncts of these FOLDNFs are equivalent to prenex normal forms whose quantifier-free parts are conjunctions of atomic and negated atomic formulae (= Herbrand formulae). In contrast to the usual algorithms for Herbrand formulae, neither skolemization nor unification algorithms with function symbols are applied. Instead, a procedure is described that (...) rests on nothing but equivalence transformations within pure first-order logic (FOL). This procedure involves the application of a calculus for negative normal forms (the NNF-calculus) with A -||- A & A (= &I) as the sole rule that increases the complexity of given FOLDNFs. The described algorithm illustrates how, in the case of Herbrand formulae, decision problems can be solved through a systematic search for proofs that reduce the number of applications of the rule &I to a minimum in the NNF-calculus. In the case of Herbrand formulae, it is even possible to entirely abstain from applying &I. Finally, it is shown how the described procedure can be used within an optimized general search for proofs of contradiction and what kind of questions arise for a &I-minimal proof strategy in the case of a general search for proofs of contradiction. (shrink)

In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but (...) more on the philosophical and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction. (shrink)

In order to fulfil their essential roles as the bearers of truth and the relata of logical relations, propositions must be public and shareable. That requirement has favoured Platonist and other nonmental views of them, despite the well-known problems of Platonism in general. Views that propositions are mental entities have correspondingly fallen out of favour, as they have difficulty in explaining how propositions could have shareable, objective properties. We revive a mentalist view of propositions, inspired by Artificial Intelligence work (...) on perceptual algorithms, which shows how perception causes persistent mental entities with shareable properties that allow them to fulfil the traditional roles of (one core kind of) propositions. The clustering algorithms implemented in perception produce outputs which are (implicit) atomic propositions in different minds. Coordination of them across minds proceeds by game-theoretic processes of communication. The account does not rely on any unexplained notions such as mental content, representation, or correspondence (although those notions are applicable in philosophical analysis of the result). (shrink)