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)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, (...) but have been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

ABSTRACT A complete axiomatic system CTLrp is introduced for a temporal logic for finitely branching ω+ -trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTLrp. In particular, that yields a complete axiomatization for the translations of all valid CTL*-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more (...) expressive medium for reasoning about branching time. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is (...) important that the participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. Keywords Epistemic logic - Cognitive science - Intelligent interaction - Cognitive modeling. (shrink)

In this paper, we provide a semantics for a range of positive substructural logics, including both logics with and logics without modal connectives. The semantics is novel insofar as it is meant to explicitly capture the computational flavor of these logics, and to do so in a way that builds in both nondeterministic and nonconcurrent computational processes.

This paper makes a novel linkage between the multiple-computations theorem in philosophy of mind and Landauer’s principle in physics. The multiple-computations theorem implies that certain physical systems implement simultaneously more than one computation. Landauer’s principle implies that the physical implementation of “logically irreversible” functions is accompanied by minimal entropy increase. We show that the multiple-computations theorem is incompatible with, or at least challenges, the universal validity of Landauer’s principle. To this end we provide accounts of both ideas in terms of (...) low-level fundamental concepts in statistical mechanics, thus providing a deeper understanding of these ideas than their standard formulations given in the high-level terms of thermodynamics and cognitive science. Since Landauer’s principle is pivotal in the attempts to derive the universal validity of the second law of thermodynamics in statistical mechanics, our result entails that the multiple-computations theorem has crucial implications with respect to the second law. Finally, our analysis contributes to the understanding of notions, such as “logical irreversibility,” “entropy increase,” “implementing a computation,” in terms of fundamental physics, and to resolving open questions in the literature of both fields, such as: what could it possibly mean that a certain physical process implements a certain computation. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a (...) flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache & Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and (...) the indeterminacy present in various real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation. (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 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)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, (...) and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

The classical theory of computation does not represent an adequate model of reality for simulation in the social sciences. The aim of this paper is to construct a methodological perspective that is able to conciliate the formal and empirical logic of program verification in computer science, with the interpretative and multiparadigmatic logic of the social sciences. We attempt to evaluate whether social simulation implies an additional perspective about the way one can understand the concepts of program and computation. (...) We demonstrate that the logic of social simulation implies at least two distinct types of program verifications that reflect an epistemological distinction in the kind of knowledge one can have about programs. Computer programs seem to possess a causal capability (Fetzer, 1999) and an intentional capability that scientific theories seem not to possess. This distinction is associated with two types of program verification, which we call empirical and intentional verification. We demonstrate, by this means, that computational phenomena are also intentional phenomena, and that such is particularly manifest in agent-based social simulation. Ascertaining the credibility of results in social simulation requires a focus on the identification of a new category of knowledge we can have about computer programs. This knowledge should be considered an outcome of an experimental exercise, albeit not empirical, acquired within a context of limited consensus. The perspective of intentional computation seems to be the only one possible to reflect the multiparadigmatic character of social science in terms of agent-based computational social science. We contribute, additionally, to the clarification of several questions that are found in the methodological perspectives of the discipline, such as the computational nature, the logic of program scalability, and the multiparadigmatic character of agent-based simulation in the social sciences. (shrink)

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

(See also the separate entry for the volume itself.) This introduction has three parts. The first providing an overview of some main lines of research in deontic logic: the emergence of SDL, Chisholm's paradox and the development of dyadic deontic logics, various other puzzles/challenges and areas of development, along with philosophical applications. The second part focus on some actual and potential fruitful interactions between deontic logic, computer science and artificial intelligence. These include applications of deontic logic to (...) AI knowledge representation in legal systems, to modelling computer systems where it is expected that sub-ideal states will emerge and require countermeasures, to norm-governed human interactions with computer systems, and to the representation of some features of multi-agent systems where different agent-like computer systems interact with one another. The third and final part briefly groups and previews the papers in the anthology. (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)

Epstein and Carnielli's fine textbook on logic and computability is now in its second edition. The readers of this journal might be particularly interested in the timeline `Computability and Undecidability' added in this edition, and the included wall-poster of the same title. The text itself, however, has some aspects which are worth commenting on.

The philosophy of mind is traditionally concerned with the study of mental processes, language, the representation of knowledge and the relation of the mind shares with the body; computational complexity theory is related to the classification of computationally solvable problems (be it via execution time, storage requirements, etc...). While there are well-established links between computer science in general & the philosophy of mind, many possible solutions to traditional problems in the philosophy of mind have not yet been analyzed from (...) the more specific lens of computational complexity theory. In his paper "Why Philosophers Should Care about Computational Complexity", Scott Aaronson argues that many conventional theories of epistemology & mind implicitly make the presupposition of omniscience (by supposing that knowing base facts means a knower necessarily understands derivative facts) - he proposes that computational complexity theory could explain why this is not the case. In this paper, I argue for a theory of mental representation & epistemology compatible with Aaronson's observations on complexity theory, overcoming that presupposition of omniscience. (shrink)

Knowledge representation (KR) is actually more than representation: It involves also inference, namely inference of “new” knowledge, i.e. new facts. Logic programming is a suitable KR medium, but more often than not discussions on this programming paradigm focus on aspects other than KR. In this paper, I elaborate on the general theory of logic programming and give the essentials of two of its main implementations, to wit, Prolog and Datalog, from the viewpoint of deductive computing over knowledge bases, (...) which includes deductive programming. (shrink)

This is a presentation about the impacts of Logic and Theory of Computation. It starts by some explanations about Theory of Computation and its relations with the other subjects in science. Then we have some explanations about paradoxes and some historical points. In continuation, we present some of the most important paradoxes. Forthcoming, Five subjects around the relations between Logic and Theory of computation is introduced. Finally, we present a new approach to solve P vs NP problem via (...) Paradoxes (Presentation 6/20/2022 In Persian, Online seminar of The Iranian Association for Logic (IAL) . (shrink)

Critical in the computationalist account of the mind is the phenomenon called computational or computer simulation of human thinking, which is used to establish the theses that human thinking is a computational process and that computing machines are thinking systems. Accordingly, if human thinking can be simulated computationally then human thinking is a computational process; and if human thinking is a computational process then its computational simulation is itself a thinking process. This paper shows that (...) the said phenomenon—the computational simulation of human thinking—is ill-conceived, and that, as a consequence, the theses that it intends to establish are problematic. It is argued that what is simulated computationally is not human thinking as such but merely its behavioral manifestations; and that a computational simulation of these behavioral manifestations does not necessarily establish that human thinking is computational, as it is logically possible for a non-computational system to exhibit behaviors that lend themselves to a computational simulation. (shrink)

Since the sixties, computational modeling has become increasingly important in both the physical and the social sciences, particularly in physics, theoretical biology, sociology, and economics. Sine the eighties, philosophers too have begun to apply computational modeling to questions in logic, epistemology, philosophy of science, philosophy of mind, philosophy of language, philosophy of biology, ethics, and social and political philosophy. This chapter analyzes a selection of interesting examples in some of those areas.

Computer-Assisted Argument Mapping (CAAM) is a new way of understanding arguments. While still embryonic in its development and application, CAAM is being used increasingly as a training and development tool in the professions and government. Inroads are also being made in its application within education. CAAM claims to be helpful in an educational context, as a tool for students in responding to assessment tasks. However, to date there is little evidence from students that this is the case. This paper outlines (...) the use of CAAM as an educational tool within an Economics and Commerce Faculty in a major Australian research university. Evaluation results are provided from students from a CAAM pilot within an upper-level Economics subject. Results indicate promising support for the use of CAAM and its potential for transferability within the disciplines. If shown to be valuable with further studies, CAAM could be included in capstone subjects, allowing computer technology to be utilised in the service of generic skill development. (shrink)

This essay examines the possibility that phenomenological laws might be implemented by a computational mechanism by carefully analyzing key passages from the Prolegomena to Pure Logic. Part I examines the famous Denkmaschine passage as evidence for the view that intuitions of evidence are causally produced by computational means. Part II connects the less famous criticism of Avenarius & Mach on thought-economy with Husserl's 1891 essay 'On the Logic of Signs (Semiotic).' Husserl is shown to reaffirm his (...) earlier opposition to associationist (Humean) and adaptationist (Darwinian) explanations of our thought-machine on the ground that they cannot reconstruct the notion of truth and its syntactic mental preservation in symbolic thought-trains. Part III reveals Husserl's interesting commitment to the idea that descriptive sciences necessarily transform into explanatory sciences on pain of contradicting the essence of science as a rational ideal. Since explanation in relation to phenomenology means causal explanation, and causal explanation in the form of the Denkmaschine accounts for phenomenological intuition, it is inferred that the rationally compelling ideal of explanatory science requires a computationalist reading of the subsequent logical investigations. (shrink)

Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still valid today. (...) This paper proposes that transcendental philosophy was a key inspiration for the development of logic diagrams and that such diagrams can be employed in transcendental arguments, even after the linguistic turn. (shrink)

Argument mapping is a way of diagramming the logical structure of an argument to explicitly and concisely represent reasoning. The use of argument mapping in critical thinking instruction has increased dramatically in recent decades. This paper overviews the innovation and provides a procedural approach for new teaches wanting to use argument mapping in the classroom. A brief history of argument mapping is provided at the end of this paper.

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational (...) content is extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing. (shrink)

Scientists and engineers seek to understand how real-world systems work and could work better. Any modeling method devised for such purposes must simplify reality. Ideally, however, the modeling method should be flexible as well as logically rigorous; it should permit model simplifications to be appropriately tailored for the specific purpose at hand. Flexibility and logical rigor have been the two key goals motivating the development of Agent-based Computational Economics (ACE), a completely agent-based modeling method characterized by seven specific modeling (...) principles. This perspective provides an overview of ACE, a brief history of its development, and its role within a broader spectrum of experiment-based modeling methods. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a chase with as (...) many twists and turns as a thriller. At the end of the story is a new principle for designing programming languages that will guide computers into the 21st century. -/- For my money, Gentzen’s natural deduction and Church’s lambda calculus are on a par with Einstein’s relativity and Dirac’s quantum physics for elegance and insight. And the maths are a lot simpler. I want to show you the essence of these ideas. I’ll need a few symbols, but not too many, and I’ll explain as I go along. -/- To simplify, I’ll present the story as we understand it now, with some asides to fill in the history. First, I’ll introduce Gentzen’s natural deduction, a formalism for proofs. Next, I’ll introduce Church’s lambda calculus, a formalism for programs. Then I’ll explain why proofs and programs are really the same thing, and how simplifying a proof corresponds to executing a program. Finally, I’ll conclude with a look at how these principles are being applied to design a new generation of programming languages, particularly mobile code for the Internet. (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)

Detractors of Searle’s Chinese Room Argument have arrived at a virtual consensus that the mental properties of the Man performing the computations stipulated by the argument are irrelevant to whether computational cognitive science is true. This paper challenges this virtual consensus to argue for the first of the two main theses of the persons reply, namely, that the mental properties of the Man are what matter. It does this by challenging many of the arguments and conceptions put forth by (...) the systems and logical replies to the Chinese Room, either reducing them to absurdity or showing how they lead, on the contrary, to conclusions the persons reply endorses. The paper bases its position on the Chinese Room Argument on additional philosophical considerations, the foundations of the theory of computation, and theoretical and experimental psychology. The paper purports to show how all these dimensions tend to support the proposed thesis of the persons reply. (shrink)

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on (...) the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argu- ment’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools ef- fectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments. (shrink)

In this article, I outline a logic of design of a system as a specific kind of conceptual logic of the design of the model of a system, that is, the blueprint that provides information about the system to be created. In section two, I introduce the method of levels of abstraction as a modelling tool borrowed from computer science. In section three, I use this method to clarify two main conceptual logics of information inherited from modernity: Kant’s (...) transcendental logic of conditions of possibility of a system, and Hegel’s dialectical logic of conditions of in/stability of a system. Both conceptual logics of information analyse structural properties of given systems. Strictly speaking, neither is a conceptual logic of information about the conditions of feasibility of a system, that is, neither is a logic of information as a logic of design. So, in section four, I outline this third conceptual logic of information and then interpret the conceptual logic of design as a logic of requirements, by introducing the relation of “sufficientisation”. In the conclusion, I argue that the logic of requirements is exactly what we need in order to make sense of, and buttress, a constructionist approach to knowledge. (shrink)

While Thomas Kuhn's theory of scientific revolutions does not specifically deal with validation, the validation of simulations can be related in various ways to Kuhn's theory: 1) Computer simulations are sometimes depicted as located between experiments and theoretical reasoning, thus potentially blurring the line between theory and empirical research. Does this require a new kind of research logic that is different from the classical paradigm which clearly distinguishes between theory and empirical observation? I argue that this is not the (...) case. 2) Another typical feature of computer simulations is their being ``motley'' (Winsberg 2003) with respect to the various premises that enter into simulations. A possible consequence is that in case of failure it can become difficult to tell which of the premises is to blame. Could this issue be understood as fostering Kuhn's mild relativism with respect to theory choice? I argue that there is no need to worry about relativism with respect to computer simulations, in particular. 3) The field of social simulations, in particular, still lacks a common understanding concerning the requirements of empirical validation of simulations. Does this mean that social simulations are still in a pre-scientific state in the sense of Kuhn? My conclusion is that despite ongoing efforts to promote quality standards in this field, lack of proper validation is still a problem of many published simulation studies and that, at least large parts of social simulations must be considered as pre-scientific. (shrink)

The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper assessment of the computational capacity of pyramidal neurons, we have analyzed an extensive dataset of three-dimensional digital reconstructions from the NeuroMorphoOrg database, and quantified basic dendritic or axonal morphometric measures in different regions and layers (...) of the mouse, rat or human cerebral cortex. Physical estimates of the total number and type of ions involved in neuronal electric spiking based on the obtained morphometric data, combined with energetics of neurotransmitter release and signaling fueled by glucose consumed by the active brain, support highly efficient cerebral computation performed at the thermodynamically allowed Landauer limit for implementation of irreversible logical operations. Individual proton tunneling events in voltage-sensing S4 protein alpha-helices of Na+, K+ or Ca2+ ion channels are ideally suited to serve as single Landauer elementary logical operations that are then amplified by selective ionic currents traversing the open channel pores. This miniaturization of computational gating allows the execution of over 1.2 zetta logical operations per second in the human cerebral cortex without combusting the brain by the released heat. (shrink)

The content of this paper is an elaboration of Hubert L. Dreyfus’s philosophical critique of Artificial Intelligence (AI), computers and the internet. Hubert L. Dreyfus (1929-2017) is Ua SA philosopher and alumni of Harvard University who teach at the Massachusetts Institute of Technology (MIT) and University of California, Berkeley. He is a phenomenological philosopher who criticize computer researchers and the artificial intelligence community. In 1965, Dreyfus wrote an article for Rand Corporation titled “Alchemy and Artificial Intelligence” which criticizes the masterminds (...) of Artificial Intelligence. Dreyfus also criticized the order of computers via two books: (1) What Computers Can’t Do (1972) and (2) What Computers Stills Can’t Do (1992). He favored human intuition rather than the computer logic in his book Mind over Machine: The Power of Human Intuition and Expertise in the Era of the Computer (1986). In 2001, Dreyfus wrote a book On the Internet, which considers the prominent phenomenon in the recent Industry 4.0. By elaborating on Dreyfus’s philosophy on the computer, artificial intelligence, and the internet, we will know the philosophical debate on the result of industry 3.0 (computer and artificial intelligence) and 4.0 (artificial intelligence and internet). Moreover, we will know the relation between humans and those industrial products. (shrink)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking (...) at how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

Part I of this paper outlined the three standard approaches to the teaching of critical thinking: the normative (or philosophical), cognitive psychology, and educational taxonomy approaches. The paper contrasted these with the visualisation approach; in particular, computer-aided argument mapping (CAAM), and presented a detailed account of the CAAM methodology and a theoretical justification for its use. This part develops further support for CAAM. A case is made that CAAM improves critical thinking because it minimises the cognitive burden of prose and (...) the demands that arguments in prose typically place on memory. CAAM also has greater usability, complements the imperfect human cognitive system, and adopts a logic of semi-formality which is both natural and intuitive. The paper claims that CAAM is an important advance given that traditional stand-alone critical thinking courses do not teach critical thinking as well as they as they are assumed to do. It is also important given that tertiary education fails to deliver improvements in critical thinking gains for too many students. The paper outlines results from a number of empirical studies that demonstrate that CAAM yields robust gains in critical thinking as measured by independent tests. Students themselves also believe CAAM to be beneficial as noted in coded responses to surveys. I conclude the paper by comparing the traditional approaches to the teaching of critical thinking to the visualisation approach. I argue that CAAM should taken seriously in the context of contemporary educational practices. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part (...) of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

I show that the indeterminacy problem for computational structuralists is in fact far more problematic than even the harshest critic of structuralism has realised; it is not a bullet which can be bitten by structuralists as previously thought. Roughly, this is because the structural indeterminacy of logic-gates such as AND/OR is caused by the structural identity of the binary computational digits 0/1 themselves. I provide a proof that pure computational structuralism is untenable because structural indeterminacy entails (...) absurd consequences - namely, that there is only one binary computational digit. I conclude that accounting for individuation is a more important desiderata for a theory of computation than even that of triviality. -/- . (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined dynamically (...) during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (shrink)

The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is with (...) computing, which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine. (shrink)

Formalizing commonsense knowledge for reasoning about time has long been a central issue in AI. It has been recognized that the existing formalisms do not provide satisfactory solutions to some fundamental problems, viz. the frame problem. Moreover, it has turned out that the inferences drawn do not always coincide with those one had intended when one wrote the axioms. These issues call for a well-defined formalism and useful computational utilities for reasoning about time and change. Yoav Shoham of Stanford (...) University introduced in his 1986 Yale doctoral thesis an appealing temporal nonmonotonic logic and identified a class of theories, causal theories, which have computationally simple model-theoretic properties. This paper is a study towards building upon Shoham's work on causal theories. We concentrate on improving computational aspects of causal theories while preserving their model-theoretic properties. (shrink)

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we (...) analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (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)

Digital computers carry out algorithms coded in high level programs. These abstract entities determine what happens at the physical level: they control whether electrons flow through specific transistors at specific times or not, entailing downward causation in both the logical and implementation hierarchies. This paper explores how this is possible in the light of the alleged causal completeness of physics at the bottom level, and highlights the mechanism that enables strong emergence (the manifest causal effectiveness of application programs) to occur. (...) Although synchronic emergence of higher levels from lower levels is manifestly true, diachronic emergence is generically not the case; indeed we give specific examples where it cannot occur because of the causal effectiveness of higher level variables. (shrink)

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...) evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert’s program due to Simpson [1988], and predicativism in the extended form due to Feferman and Schütte. -/- Shore [2010, 2013] proposes that equivalences in reverse mathematics be proved in the same way as inequivalences, namely by considering only omega-models of the systems in question. Shore refers to this approach as computational reverse mathematics. This paper shows that despite some attractive features, computational reverse mathematics is inappropriate for foundational analysis, for two major reasons. Firstly, the computable entailment relation employed in computational reverse mathematics does not preserve justification for the foundational programs above. Secondly, computable entailment is a Pi-1-1 complete relation, and hence employing it commits one to theoretical resources which outstrip those available within any foundational approach that is proof-theoretically weaker than Pi-1-1-CA0. (shrink)

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are (...) developed, and mapped to the ontology of time. (shrink)

Emotions and feelings (i.e. affects) are a central feature of human behavior. Due to complexity and interdisciplinarity of affective phenomena, attempts to define them have often been unsatisfactory. This article provides a simple logical structure, in which affective concepts can be defined. The set of affects defined is similar to the set of emotions covered in the OCC model, but the model presented in this article is fully computationally defined, whereas the OCC model depends on undefined concepts. Following Matthis, affects (...) are seen as unconscious, emotions as preconscious and feelings as conscious. Affects are thus a superclass of emotions and feelings with regards to consciousness. A set of affective states and related affect-specific behaviors and strategies can be defined with unconscious affects only. -/- In addition, affects are defined as processes of change in the body state, that have specific triggers. For example, an affect of hope is defined as a specific body state that is triggered when the agent is becomes informed about a future event, that is positive with regards to the agent’s needs. -/- Affects are differentiated from each other by types of causing events. Affects caused by unexpected positive, neutral and negative events are delight, surprise and fright, respectively. Affects caused by expected positive and negative future events are hope and fear. -/- Affects caused by expected past events are as follows: satisfaction results from a positive expectation being fulfilled, disappointment results from a positive expectation not being fulfilled, fears-confirmed results from a negative expectation being fulfilled, and relief results from a negative expectation not being fulfilled. Pride is targeted towards a self-originated positive event, and shame towards a self-originated negative event. Remorse is targeted towards a self-originated action causing a negative event. Pity is targeted towards a liked agent experiencing a negative event, and happy-for towards a liked agent experiencing a positive event. Resentment is targeted towards a disliked agent experiencing a positive event, and gloating towards a disliked agent experiencing a negative event. An agent is liked/loved if it has produced a net utility greater than zero, and disliked/hated if the net utility is lower than zero. An agent is desired if it is expected to produce a positive net utility in the future, and disliked if the expected net utility is negative. -/- The above model for unconscious affects is easily computationally implementable, and may be used as a starting point in building believable simulation models of human behavior. The models can be used as a starting point in the development of computational psychological, psychiatric, sociological and criminological theories, or in e.g. computer games. -/- [please cite using the arXiv url below.]. (shrink)