The purpose of this article is to present an evidence-supported curriculum covering the fundamentals of logic, reasoning, and argumentation skills to address the emphasized basic knowledge, skills, and abilities required to be scientifically literate, which will prepare the public to understand and engage with science meaningfully. An analytic-synthetic approach toward understanding the notion of public is taken using a theoretical biomimetics framework that identifies naturally occurring objects or phenomena that descriptively captures the essence of a construct to facilitate creative (...) problem-solving. In the present case, the problem being solved is how to reconcile what is meant by public, how it ought to be interpreted, determining the diverse levels of confidence in science that exist, and various understandings of science all with one another. The results demonstrate there is an inherent denotative-connotative inconsistency in the traditional notion of public that can be explicated through the concept of a fractal allowing for comprehension of the relationship between public confidence in, and understanding of, science. (shrink)

Cognitive scientists used to deem reasoning either as a higher cognitive process based on the manipulation of abstract rules or as a higher cognitive process that is stochastic rather than involving abstract rules. I maintain that these different perspectives are closely intertwined with a theoretical and methodological endorsement of either cognitivism or connectionism. Cognitivism and connectionism represent two prevailing and opposed paradigms in cognitive science. I aim to extoll the virtues of connectionist models of enthymematic reasoning by following (...) means: via the phenomenon of creative enthymeme, viz. the inference where one cannot even articulate the missing premise, I introduce a connectionist mechanism of pattern recognition as underlying expertise; via Gestalt switch or Gestalt click, I demonstrate how differences in pattern recognition of an expert and a novice can be construed as qualitatively different, and not merely a matter of faster reasoning. (shrink)

In a world filled with information overload and complex problems, the ability to think logically is a superpower. "A Little More Logical" is your guide to mastering this essential skill. This engaging and accessible open educational resource is perfect for students, teachers, and lifelong learners who want to improve their critical thinking abilities and make better decisions in all aspects of life. -/- Through a series of fun and interactive chapters, "A Little More Logical" covers a wide range (...) of topics, from the basics of constructing sound arguments to the application of logic in fields like ethics, science, and computing. You'll learn how to spot and avoid common fallacies, analyze real-world arguments, and use logical reasoning to solve problems and make informed choices. -/- But this book isn't just about abstract concepts – it's about the human story behind logic. You'll discover the fascinating lives and ideas of diverse thinkers, from ancient philosophers to modern-day pioneers, who have shaped the development of logical reasoning throughout history. With thought-provoking examples, engaging exercises, and plenty of humor along the way, "A Little More Logical" makes the study of logic both rigorous and entertaining. -/- Whether you're a student looking to ace your philosophy class, a teacher searching for high-quality educational resources, or a curious reader who wants to sharpen your mind, "A Little More Logical" is the perfect companion on your journey to becoming a more effective thinker. Unlock the power of logical thinking today with this one-of-a-kind open educational resource! (shrink)

The Concept of Life and Death of Chuang-tzu have inherited and developed Confucianism and Taoism thoughts, establishing Ontological foundation of "Life - Body", distinguishing the transcendental concept of "Dead Heart" and the empirical concept of "Death Body", as well as proposing the thought of "Equivalence of Life and Death" finally. The logic Reasoning of Chuang-tzu "Equivalence of Life and Death", start from constructing the equal status of "Life" and “Death" from ontological argument. Life and Death then are reduced to (...) be a natural phenomenon to dispel its mystery. With emphasizing the social connotation of life and death, the difference between them has been removed, and finally the Thought experiment of "Chuang-tzu dreaming butterfly" has deepened the idea of "Equivalence of Life and Death". The Ideological Characteristic of the Concept of Life and Death of Chuang-tzu mainly reflects in the aspects of Ontology, Epistemology and Ethical practice. (shrink)

Logical pluralism is the view that there is more than one correct logic. A key objection to logical pluralism is that it collapses into monism. The core of the Collapse Objection is that only the pluralist’s strongest logic does any genuine normative work; since a logic must do genuine normative work, this means that the pluralist is really a monist, who is committed to her strongest logic being the one true logic. This paper considers a neglected question in (...) the collapse debate: what is it for a logic to do genuine normative work? As well as having wider upshot for the connection between logic and normativity, grappling with this question provides a new response to the Collapse Objection on behalf of the pluralist. I suggest that we should allow logics to generate pro tanto reasons in a way that bears not just on combinations of attitudes but on how an agent’s attitudes are based on one another. This motivates adopting normative principles that allow the pluralist’s weaker logics to earn their normative keep. Rather than being ad hoc, these principles capture a sense in which good reasoning goes beyond the consistency of an agent’s attitudes. Good reasoning is also concerned with how an agent’s attitudes are based on one another. (shrink)

Logic has been a—disputed—ingredient in the emergence and development of the now very large field known as knowledge representation and reasoning. In this book (in progress), I select some central topics in this highly fruitful, albeit controversial, association (e.g., non-monotonic reasoning, implicit belief, logical omniscience, closed world assumption), identifying their sources and analyzing/explaining their elaboration in highly influential published work.

This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed here, the (...) “Logic of Many” and the “Logic of Plausibility”, that characterize assertions of the kind “many”, and “for a good number of”. Although the notion of simple majority (“more than half”) can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on evidence sets, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers as notions of families of principal filters and reduced topologies, respectively. We prove that both systems are conservative extensions of classical logic that preserve important properties, such as soundness and completeness. Some additional perspectives connecting our approach to flexible reasoning through modulated logics to epistemology and social choice theory are also discussed. (shrink)

By a reasoned change in logic I mean a change in the logic with which you make inferences that is based on your evidence. An argument sourced in recently published material Kripke lectured on in the 1970s, and dubbed the Adoption Problem by Birman (then Padró) in her 2015 dissertation, challenges the possibility of reasoned changes in logic. I explain why evidentialists should be alarmed by this challenge, and then I go on to dispel it. The Adoption Problem rests on (...) a failure to distinguish between logical principles such as Universal Instantiation and Modus Ponens which might or might not govern your inferences with superficially similar laws which must govern your cognitive architecture. (shrink)

In this chapter, we begin by sketching in the broadest possible strokes the ideas behind two formal systems that have been introduced with to goal of explicating the ways in which reasons interact to support the actions and conclusions they do. The first of these is the theory of defeasible reasoning developed in the seminal work of Pollock; the second is a more recent theory due to Horty, which adapts and develops the default logic introduced by Reiter to provide (...) an account of reasons. However, the implementations are complex enough, in both cases, to prevent anything more than this sketch. And we would not want to give the impression that we think that work on the logic of reasons must follow the path mapped out in either of these theories—indeed, we feel that the field is wide open. In the remainder of the chapter, therefore, will concentrate on a number of issues bearing on the logic of reasons that are either not treated in the work of Pollock and Horty, or whose treatment there is, we feel, either inadequate or incomplete. These are: first, the question of whether it is necessary to understand logical interactions among reasons themselves, rather than simply between reasons and the actions or conclusions they support, and if so, what principles might govern these interactions; second, priority relations among reasons and the notion of reason accrual; and third, some problems posed by undercutting defeat. (shrink)

This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human (...) subjects who produce the outwardly correct ‘backward induction answer’ use a different internal reasoning strategy to achieve it. The paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics help to precisely distinguish different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects. The syntactic framework of the formal system provides a generic way of constructing computational cognitive models of the participants of the Marble Drop game. (shrink)

As the journal is effectively defunct, I am uploading a full-text copy, but only of my abstract and article, and some journal front matter. -/- Note that the pagination in the PDF version differs from the official pagination because A4 and 8.5" x 11" differ. -/- Traditionally, imperatives have been handled with deontic logics, not the logic of propositions which bear truth values. Yet, an imperative is issued by the speaker to cause (stay) actions which change the state of affairs, (...) which is, in turn, described by propositions that bear truth values. Thus, ultimately, imperatives affect truth values. In this paper, we put forward an idea that allows us to reason with imperatives using classical logic by constructing a one-to-one correspondence between imperatives and a particular class of declaratives. (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)

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata (...) of first order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

This paper explores the question of what logic is not. It argues against the wide spread assumptions that logic is: a model of reason; a model of correct reason; the laws of thought, or indeed is related to reason at all such that the essential nature of the two are crucially or essentially co-illustrative. I note that due to such assumptions, our current understanding of the nature of logic itself is thoroughly entangled with the nature of reason. I show that (...) most arguments for the presence of any sort of essential re- lationship between logic and reason face intractable problems and demands, and fall well short of addressing them. These arguments include those for the notion that logic is normative for reason (or that logic and correct reason are in some way the same thing), that logic is some sort of description of correct reason and that logic is an abstracted or idealised version of correct reason. A strong version of logical realism is put forward as an alternative view, and is briefly explored. (shrink)

This book presents a philosophical conception of logic -- "logical expressivism"-- according to which the role of logic is to make explicit reason relations, which are often neither monotonic nor transitive. It reveals new perspectives on inferential roles, sequent calculi, representation, truthmakers, and many extant logical theories.

For years, the European world saw millions of swans, and all of them without exception were white. If inductive reasoning is valid, one may conclude that all swans are white. However, this would be incorrect: in 1667 Dutch explorer Willem de Vlamingh observed black swans in Australia, falsifying the hypothesis that all swans are white. While often used as a cautionary tale for the use of induction, such as with Popper’s falsification principle, I want to explore a slightly different (...) idea: does the existence of fabricated or otherwise failed accounts of Black swans give me a reason to ignore future arguments or doubt their existence? I argue that while faulty or fabricated reports do not give us a logical reason to reject a claim, they can give us a practical one for refusing to consider future arguments. This practical vs logical distinction gives an inductive reason for believing that future arguments will be invalid, but keeps one from being able to necessarily deny the claim in question without further argumentation. (shrink)

According to a prevalent view among philosophers formal logic is the philosopher’s main tool to assess the validity of arguments, i.e. the philosopher’s ars iudicandi. By drawing on a famous dispute between Russell and Strawson over the validity of a certain kind of argument – of arguments whose premises feature definite descriptions – this paper casts doubt on the accuracy of the ars iudicandi conception. Rather than settling the question whether the contentious arguments are valid or not, Russell and Strawson, (...) upon discussing the proper logical analysis of definite descriptions, merely contrast converse informal validity assessments rendered explicit by nonequivalent logical for-malizations. (shrink)

We present a number of modal logics to reason about group norms. As a preliminary step, we discuss the ontological status of the group to which the norms are applied, by adapting the classification made by Christian List of collective attitudes into aggregated, common, and corporate attitudes. Accordingly, we shall introduce modality to capture aggregated, common, and corporate group norms. We investigate then the principles for reasoning about those types of modalities. Finally, we discuss the relationship between group norms (...) and types of collective responsibility. (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)

Building on the notational principles of C. S. Peirce’s graphical logic, Pietarinen has tried to develop a propositional logic unfolding in the medium of sound. Apart from its intrinsic interest, this project serves as a concrete test of logic’s range. However, I argue that Pietarinen’s inaugural proposal, while promising, has an important shortcoming, since it cannot portray double-negation without thereby portraying a contradiction.

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the (...) importance of a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)

In this Dissertation, we examine a handful of related themes in the philosophy of logic and mathematics. We take as a starting point the deeply philosophical, and—as we argue, deeply Kantian—views of L.E.J. Brouwer, the founder of intuitionism. We examine his famous first act of intuitionism. Therein, he put forth both a critical and a constructive idea. This critical idea involved digging a philosophical rift between what he thought of himself as doing and what he thought of his contemporaries, specifically (...) Hilbert, as doing. He sought to completely separate mathematics from mathematical language, and thereby logic. In chapter 3, we examine the philosophical foundations for this separation. Artemov Artemov (2001) articulates what we might think of as constructive propositional reasoning in a formal system that augments classical propositional logic with a theory of proofs. In doing this, instead of using just one type of object to characterize constructive reasoning, he uses two; propositions and proofs. In chapter 4, we explore the extent to which it might make sense to think of classical propositional reasoning as instead a theory that has two types of objects in the Artemov style. In chapters 5 and 6, we examine two specific case studies; we look at two philosophical phenomena that admit of formal characterizations and then propose those. In both cases, we focus on predicate style treatments of modality. (shrink)

The paper argues that logical reasoning is what constitutes critical thinking because reasoning is normative, and logic provides a norm for reasoning. If a logical way of thinking is simply the same thing as reasoning, then the only limit or constraint of reasoning is the nature of the (logical) “rule” the kind of which is engaged with the practice of reasoning; rather than with either a component of social context or a (...) com- ponent of a purely non-inferential or “immediate” perception of a situation which is called sensitivity toward an object alone. However, such components are built into my analysis of what “reasoning” is. An approach to critical thinking being employed here is “an agent-based approach”. This paper also aims to pave the way for a further discussion on the limit of reasoning in a way that is relevant to the question of how critical thinking or reasoning should be taught in higher education. (shrink)

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to apply (...) general logical principles in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules have (...) logical contents, or following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine’s early work, and consider two attempts to reply to Quine. (shrink)

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘p is a reason for q’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts (...) of conditionals. (shrink)

There are two competing theoretical frameworks with which cognitive sciences examines how people reason. These frameworks are broadly categorized into logic and probability. This paper reports two applied experiments to test which framework explains better how people reason about evidence in criminal cases. Logical frameworks predict that people derive conclusions from the presented evidence to endorse an absolute value of certainty such as ‘guilty’ or ‘not guilty’ (e.g., Johnson-Laird, 1999). But probabilistic frameworks predict that people derive conclusions from the (...) presented evidence in order that they may use knowledge of prior instances to endorse a conclusion of guilt which varies in certainty (e.g., Tenenbaum, Griffiths, & Kemp, 2006). Experiment 1 showed that reasoning about evidence of prior instances, such as disclosed prior convictions, affected participants’ underlying ratings of guilt. Participants’ guilt ratings increased in certainty according to the number of disclosed prior convictions. Experiment 2 showed that participants’ reasoning about evidence of prior convictions and some forensic evidence tended to lead participants to endorse biased ‘guilty’ verdicts when rationally the evidence does not prove guilt. Both results are predicted by probabilistic frameworks. The paper considers the implications for logical and probabilistic frameworks for reasoning in the real world. (shrink)

We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types of (...) class='Hi'>reasoning supported by DIO one can distinguish both (1) basic reasoning about general structures in reality and (2) the domain-specific reasoning of experts. We here propose a clarification of this important distinction between (realist) reasoning on the basis of an ontology and rule-based inferences on the basis of an expert’s view. (shrink)

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN , we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the (...) three categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. (shrink)

“Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of logic, epistemology, philosophy and history (...) of science, while bringing together scholars in the fields of philosophy, logic, mathematics, computer science and other disciplines who have contributed significantly to what Studia Logica is today and to what CLE has achieved in its four decades of existence. It intends to celebrate CLE’s strong influence in Brazil and Latin America and the tradition of investigating formal methods inspired by, and devoted to, philosophical views, as well as philosophical problems approached by means of formal methods. The title of the event commemorates one of the three main areas of CLE, what has been called the “Brazilian school of paraconsistency”, combining such a pluralist view about logic and reasoning. (shrink)

In recent years, the human ability to reasoning about mental states of others in order to explain and predict their behavior has come to be a highly active area of research. Researchers from a wide range of fields { from biology and psychology through linguistics to game theory and logic{ contribute new ideas and results. This interdisciplinary workshop, collocated with the Thirteenth International Conference on Theoretical Aspects of Rationality and Knowledge (TARK XIII), aims to shed light on models of (...) social reasoning that take into account realistic resource bounds. People reason about other people's mental states in order to understand and predict the others' behavior. This capability to reason about others' knowledge, beliefs and intentions is often referred to as theory of mind. Idealized rational agents are capable of recursion in their social reasoning, and can reason about phenomena like common knowledge. Such idealized social reasoning has been modeled by modal logics such as epistemic logic and BDI (belief, desire, intention) logics and by epistemic game theory. However, in real-world situations, many people seem to lose track of such recursive social reasoning after only a few levels. The workshop provides a forum for researchers that attempt to analyze, understand and model how resource-bounded agents reason about other minds. (shrink)

Sorensen (1992) has provided two modal-logical schemas to reconstruct the logical structure of two types of destructive thought experiments: the Necessity Refuter and the Possibility Refuter. The schemas consist of five propositions which Sorensen claims but does not prove to be inconsistent.We show that the five propositions, as presented by Sorensen, are not inconsistent, but by adding a premise (and a logical truth), we prove that the resulting sextet of premises is inconsistent. Häggqvist (2009) has provided a (...) different modal-logical schema (Counterfactual Refuter), which is equivalent to four premises, again claimed to be inconsistent. We show that this schema also is not inconsistent, for similar reasons. Again, we add another premise to achieve inconsistency. The conclusion is that all three modal-logical reconstructions of the arguments that accompany thought experiments, two by Sorensen and one by Häggqvist, have now been made rigorously correct. This may inaugurate new avenues to respond to destructive thought experiments. (shrink)

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance (...) to the correctness of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. On the proof-theoretical side, (...) two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization. (shrink)

A modal logic for representing analogical proportions is presented. This logic is a modal interpretation of H. Prade and G. Richard's homogeneous analogy. A tableaux system is given with some examples an intuitions.

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current (...) in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain. (shrink)

Neuroscience has studied deductive reasoning over the last 20 years under the assumption that deductive inferences are not only de jure but also de facto distinct from other forms of inference. The objective of this research is to verify if logically valid deductions leave any cerebral electrical trait that is distinct from the trait left by non-valid deductions. 23 subjects with an average age of 20.35 years were registered with MEG and placed into a two conditions paradigm (100 trials (...) for each condition) which each presented the exact same relational complexity (same variables and content) but had distinct logical complexity. Both conditions show the same electromagnetic components (P3, N4) in the early temporal window (250–525 ms) and P6 in the late temporal window (500–775 ms). The significant activity in both valid and invalid conditions is found in sensors from medial prefrontal regions, probably corresponding to the ACC or to the medial prefrontal cortex. The amplitude and intensity of valid deductions is significantly lower in both temporal windows (p = 0.0003). The reaction time was 54.37% slower in the valid condition. Validity leaves a minimal but measurable hypoactive electrical trait in brain processing. The minor electrical demand is attributable to the recursive and automatable character of valid deductions, suggesting a physical indicator of computational deductive properties. It is hypothesized that all valid deductions are recursive and hypoactive. (shrink)

The reasoning process of analogy is characterized by a strict interdependence between a process of abstraction of a common feature and the transfer of an attribute of the Analogue to the Primary Subject. The first reasoning step is regarded as an abstraction of a generic characteristic that is relevant for the attribution of the predicate. The abstracted feature can be considered from a logic-semantic perspective as a functional genus, in the sense that it is contextually essential for the (...) attribution of the predicate, i.e. that is pragmatically fundamental (i.e. relevant) for the predica-tion, or rather the achievement of the communicative intention. While the transfer of the predicate from the Analogue to the analogical genus and from the genus to the Primary Subject is guaranteed by the maxims (or rules of inference) governing the genus-species relation, the connection between the genus and the predicate can be complex, characterized by various types of reasoning patterns. The relevance relation can hide implicit arguments, such as an implicit argument from classification , an evaluation based on values, consequences or rules, a causal relation, or an argument from practical reasoning. (shrink)

Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance (...) two logical norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument. (shrink)

There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory (...) provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view. (shrink)

Reasoning by default is a relevant aspect of everyday life that has traditionally attracted the attention of many fields of research, from psychology to the philosophy of logic, from economics to artificial intelligence. Also in the field of law, default reasoning is widely used by lawyers, judges and other legal decision-makers. In this paper, a philosopher of language (Carlo Penco) and a philosopher of law (Damiano Canale) attempt to explore some uses of default reasoning that are scarcely (...) considered by legal theory. In particular, the dialogue dwells on the notion of literal meaning, witness testimony, and the problem of disagreement among experts in legal proceedings. The paper is intended as a sort of brain storming useful to identify new lines of research straddling philosophy of law, cognitive psychology and philosophy of language. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

My analysis here is an attempt to bring out the main through-line in the development of Bulgarian philosophy of law today. A proper account of Bulgarian philosophy of law in the 20th century requires an attempt to find, on the one hand, a solution to epistemological and methodological problems in law and, on the other, a clear-cut influence of the Kantian critical tradition. Bulgarian philosophy of law follows a complicated path, ranging from acceptance and revision of Kantian philosophy to the (...) development of interesting theories on the logic of legal reasoning. (shrink)

We intoduce a novel extension of Description Logics (DLs) of typicality by means of probabilities able to represent and reason about typical properties and defeasible inheritance in DLs.

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; (...) that it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in (...) a clear sense, non-identical to it. We argue that this phenomenon can be generalized, given the existence of logics which coincide with Classical Logic regarding a number of metainferential levels—although they are, again, clearly different systems. We claim this highlights the need to arrive at a more refined version of the Collapse Argument, which we discuss at the end of the paper. (shrink)

One of the popular albeit controversial ideas in the last century of moral philosophy is that what we ought to do is explained by our reasons. And one of the central features of reasons that accounts for their popularity among normative theorists is that they can conflict. But I argue that the fact that reasons conflict actually also poses two closely related problems for this popular idea in moral philosophy. The first problem is a generalization of a problem in deontic (...) logic concerning the existence of conflicting obligations. The second problem arises from a tension between the fact that reasons can conflict and a model of how reasons explain ‘ought’s that has been widely accepted. Having presented each of these problems, I develop a unified solution to them that is informed by results in both ethics and deontic logic. An important implication of this solution is that we must distinguish between derivative and nonderivative reasons and revise our conception how it is that reasons explain ‘ought’s. (shrink)

Data involving epistemic modals suggest that some classically valid argument forms, such as _reductio_, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a _de re–de dicto_ collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern (...) the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic. (shrink)