Khemlani et al. (2018) mischaracterize logic in the course of seeking to show that mental model theory (MMT) can accommodate a form of inference (, let us label it) they find in a high percentage of their subjects. We reveal their mischaracterization and, in so doing, lay a landscape for future modeling by cognitive scientists who may wonder whether human reasoning is consistent with, or perhaps even capturable by, reasoning in a logic or family thereof. Along the way, we note (...) that the properties touted by Khemlani et al. as innovative aspects of MMT‐based modeling (e.g., nonmonotonicity) have for decades been, in logic, acknowledged and rigorously specified by families of (implemented) logics. Khemlani et al. (2018) further declare that is “invalid in any modal logic.” We demonstrate this to be false by our introduction (Appendix A) of a new propositional modal logic (within a family of such logics) in which is provably valid, and by the implementation of this logic. A second appendix, B, partially answers the two‐part question, “What is a formal logic, and what is it for one to capture empirical phenomena?”. (shrink)

Thinking about misleading higher-order evidence naturally leads to a puzzle about epistemic rationality: If one’s total evidence can be radically misleading regarding itself, then two widely-accepted requirements of rationality come into conflict, suggesting that there are rational dilemmas. This paper focuses on an often misunderstood and underexplored response to this (and similar) puzzles, the so-called conflicting-ideals view. Drawing on work from defeasible logic, I propose understanding this view as a move away from the default metaepistemological position according to which rationality (...) requirements are strict and governed by a strong, but never explicitly stated logic, toward the more unconventional view, according to which requirements are defeasible and governed by a comparatively weak logic. When understood this way, the response is not committed to dilemmas. (shrink)

A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and (...) I show that Anselm’s treatment of counterpossible conditionals concerning the procession of the spirit from the son in Trinitarian theology represent an early foray into default logic. Thus, the mutual estrangement of eastern and western positions on the matter may not lie fundamentally in a change in dogma, but rather in a change in logic. (shrink)

This paper proposes an argumentation-based procedure for legal interpretation, by reinterpreting the traditional canons of textual interpretation in terms of argumentation schemes, which are then classified, formalized, and represented through argument visualization and evaluation tools. The problem of statutory interpretation is framed as one of weighing contested interpretations as pro and con arguments. The paper builds an interpretation procedure by formulating a set of argumentation schemes that can be used to comparatively evaluate the types of arguments used in cases of (...) contested statutory interpretation in law. A simplified version of the Carneades Argumentation System is applied in a case analysis showing how the procedure works. A logical model for statutory interpretation is finally presented, covering pro-tanto and all-things-considered interpretive conclusions. (shrink)

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...) present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology (...) is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

A dynamic semantics for iffy oughts offers an attractive alternative to the folklore that Chisholm's paradox enforces an unhappy choice between the intuitive inference rules of factual and deontic detachment. The first part of the story told here shows how a dynamic theory about ifs and oughts gives rise to a nonmonotonic perspective on deontic discourse and reasoning that elegantly removes the air of paradox from Chisholm's puzzle without sacrificing any of the two detachment principles. The second part of the (...) story showcases two bonus applications of the framework suggested here: it offers a response to Forrester's gentle murder paradox and avoids Kolodny and MacFarlane's miners paradox about deontic reasoning under epistemic uncertainty. A comparison between the dynamic semantic proposal made in this paper and a more conservative approach combining a static semantics with a dynamic pragmatics is provided. (shrink)

This is an expository article about the solution to the frame problem proposed in 1980 by Raymond Reiter. For years, his “frame default” remained untested and suspect. But developments in some seemingly unrelated areas of computer science—logic programming and satisfiability solvers—eventually exonerated the frame default and turned it into a basis for important applications.

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine (...) to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications. (shrink)

In our approach credibility of information plays an importantrole in modeling of both belief state and belief change [4]. It turns out thatthe credibility-based consequence operators used to define the notion of beliefstate tolerate inconsistency under some conditions.

This paper is a commentary on the target article by Lokendra Shastri & Venkat Ajjanagadde [S&A]: “From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony” in same issue of the journal, pp.417–451. -/- It puts S&A's temporal-synchrony binding method in a broader context, comments on notions of pointing and other ways of associating information - in both computers and connectionist systems - and mentions types of reasoning that are a challenge to (...) S&A's system (amongst many other connectionist systems, recognizing that S&A's is much more capable as regards reasoning than most other contemporary systems). (shrink)

Gelfond and Lifschitz proposed the notion of a stable model of a logic program. We establish that the set of all stable models in a Herbrand universe of a recursive logic program is, up to recursive renaming, the set of all infinite paths of a recursive, countably branching tree, and conversely. As a consequence, the problem, given a recursive logic program, of determining whether it has at least one stable model, is Σ11-complete. Due to the equivalences established in the authors' (...) previous nonmonotone rule systems papers ), this applies equally to truth maintenance systems and default logics. (shrink)

The often observed complexity gap between the expressiveness of a logical formalism and its exponentially harder expression complexity is proven for all logical formalisms which satisfy natural closure conditions. The expression complexity of the prefix classes of second-order logic can thus be located in the corresponding classes of the weak exponential hierarchies; further results about expression complexity in database theory, logic programming, nonmonotonic reasoning, first-order logic with Henkin quantifiers and default logic are concluded. The proof method illustrates the significance of (...) quantifier-free interpretations in descriptive complexity theory. (shrink)

We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is Δ-elementary, then it is elementary. That is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. This means that classes of (...) models of circumscribed theories are either elementary or not Δ-elementary. Finally, using the previous result, we prove that, whenever a relation Pi is defined in the class of P; Z-minimal models of a first-order sentence Φ and whenever such class of P; Z-minimal models is Δ-elementary, then there is an explicit definition ψ for Pi such that the class of P; Z-minimal models of Φ is the class of models of Φ ∧ ψ. In order words, the circumscription of P in Φ with Z varied can be replaced by Φ plus this explicit definition ψ for Pi. (shrink)

In his book on fallacies, Hamblin built a very simple system for argumentation in dialogue he called the Why Because System with Questions. In his discussion of this system, he replaced the concept of burden of proof with a simpler concept of initiative, which could be described as something like getting the upper hand as the argumentation moves back and forth in the dialogue between the one party and the other. No doubt he realized that the concept of burden of (...) proof was too complex a matter to be dealt with in the limited scope of his chapter on formal dialogue systems. In this paper is shown how an extended version of Hamblin’s dialogue system provides a nice way of modeling the phenomenon of shifting of burden of proof in a dialogue, yielding a precise way of distinguishing between different kinds of burden of proof, and dealing with fallacies like the argumentum ad ignorantiam. (shrink)

The purpose of this paper is twofold. First we want to extent a specific paranormal modal logic in such a way as obtain a paraconsistent and paracomplete multimodal logic able to formalize the notions of plausibility and certainty. With this logic at hand, and this is our second purpose, we shall use a modified version of Reiter‘s default logic to build a sort of inductive logic of plausibility and certainty able to represent some basic principles of epistemic inductive reasoning, such (...) as a negative autoepistemic principle, an `error-prone feature of induction' principle and a confirmation by enumeration principle. (shrink)

ABSTRACT We investigate a logic PFD, as introduced in [FA]. In our notation, this logic is enriched with operators P> r(r € [0,1]) where the intended meaning of P> r φ is “the probability of φ (at a given world) is strictly greater than r”. We also adopt the semantics of [FA]: a class of “F-restricted probabilistic kripkean models”. We give a completeness proof that essentially differs from that in [FA]: our “peremptory lemma” (a lemma in PFD rather than about (...) it) facilitates the construction of a canonical model for PFD considerably. We show that this construction can be carried out using only finitary means, and also give a filtration-technique for the intended models. We then define an alternative (in some sense more natural) semantics for the logic, and show some of its properties. Finally, we prove decidability of the logic. (shrink)

The paper examines locative expressions and shows that an adequate account of their meaning must be based on two essential understandings: First, the simple spatial relation, often given as the meaning of the spatial prepositions, is only an “ideal” from which there are deviations in context; second, a level of “geometric conceptualization” mediates between “the world as it is” and language. Pragmatic “near principles” are formulated to explain some deviations from the ideal and several other apparent irregularities of prepositional use. (...) A set of “use types” of the ideal meaning is proposed to account for conventional aspects of locative meaning. The paper concludes with a discussion of the consequences of this description of locative expressions for artificial intelligence and linguistics. (shrink)

In this two-parts paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics  including normal modal logics, paranormal modal logics and classical logic can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that paranormal modal logic is a formalization of (...) the notions of skeptical and credulous plausibility. (shrink)

Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also suggested that an appeal to such factors can help deal with problems facing existing accounts of actual causation. This article develops a flexible formal framework for incorporating defaults, typicality, and normality into an account of actual causation. The resulting account takes actual causation to be both graded and (...) comparative. We then show how our account would handle a number of standard cases. 1 Introduction2 Causal Models3 The HP Definition of Actual Causation4 The Problem of Isomorphism5 Defaults, Typicality, and Normality6 Extended Causal Models7 Examples7.1 Omissions7.2 Knobe effects7.3 Causes versus background conditions7.4 Bogus prevention7.5 Causal chains7.6 Legal doctrines of intervening causes7.7 Pre-emption and short circuits8 Conclusion. (shrink)

A number of authors have suggested that a conditional analysis of dispositions must take roughly the following form: Thing X is disposed to produce response R to stimulus S just in case, if X were exposed to S and surrounding circumstances were auspicious, then X would produce R. The great challenge is cashing out the relevant notion of ‘auspicious circumstances’. I give a general argument which entails that all existing conditional analyses fail, and that there is no satisfactory way to (...) define ‘auspicious circumstances’ just in terms of S, R, and X. Instead, I argue that the auspicious circumstances C for the manifestation of a disposition constitute a third irreducible element of that disposition, and that to pick out (or to ‘individuate’) that disposition one must specify C along with S and R. This enables a new conditional analysis of dispositions that gives intuitively satisfying answers in cases that pose problems for other approaches. (shrink)

Arthur Prior was a truly philosophical logician. Though he believed formal logic to be worthy of study in its own right, of course, the source of Prior’s great passion for logic was his faith in its capacity for clarifying philosophical issues, untangling philosophical puzzles, and solving philosophical problems. Despite the fact that he has received far less attention than he deserves, Prior has had a profound influence on the development of philosophical and formal logic over the past forty years, a (...) fact to which the present volume bears eloquent witness. The genesis of the volume was the 1989 Arthur Prior Memorial Conference, held appropriately enough at the University of Canterbury in Christchurch, New Zealand, where Prior had his first appointment in philosophy. However, this is not a volume of proceedings. Only eight of the twenty-two essays were actually presented at the conference. The rest were solicited by the editor specially for the volume. The subtitle—Essays on the Legacy of Arthur Prior—is an appropriate one. Few of the essays devote much space to Prior’s work per se. Rather, most address issues that, if not first raised by Prior, were revisited by him and subjected to his typically keen and distinctively original analysis. The papers themselves divide pretty evenly into the technical and the less technical. In this short review I will focus on the latter. (shrink)

In this paper we will analyse the issue of defeasibility in the law, taking into account research carried out in philosophy, artificial intelligence and legal theory. We will adopt a very general idea of legal defeasibility, in which we will include all different ways in which certain legal conclusions may need to be abandoned, though no mistake was made in deriving them. We will argue that defeasibility in the law involves three different aspects, which we will call inference‐based defeasibility, process‐based (...) defeasibility, and theory‐based defeasibility. Only the integration of these three perspectives allows us to provide a satisfactory account of the role of defeasibility in legal reasoning. (shrink)

This paper argues that some traditional fallacies should be considered as reasonable arguments when used as part of a properly conducted dialog. It is shown that argumentation schemes, formal dialog models, and profiles of dialog are useful tools for studying properties of defeasible reasoning and fallacies. It is explained how defeasible reasoning of the most common sort can deteriorate into fallacious argumentation in some instances. Conditions are formulated that can be used as normative tools to judge whether a given defeasible (...) argument is fallacious or not. It is shown that three leading violations of proper dialog standards for defeasible reasoning necessary to see how fallacies work are: (a) improper failure to retract a commitment, (b) failure of openness to defeat, and (c) illicit reversal of burden of proof. (shrink)

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

Fixpoint semantics are provided for ambiguity blocking and propagating variants of Nute's defeasible logic. The semantics are based upon the well-founded semantics for logic programs. It is shown that the logics are sound with respect to their counterpart semantics and complete for locally finite theories. Unlike some other nonmonotonic reasoning formalisms such as Reiter's default logic, the two defeasible logics are directly skeptical and so reject floating conclusions. For defeasible theories with transitive priorities on defeasible rules, the logics are shown (...) to satisfy versions of Cut and Cautious Monotony. For theories with either conflict sets closed under strict rules or strict rules closed under transposition, a form of Consistency Preservation is shown to hold. The differences between the two logics and other variants of defeasible logic—specifically those presented by Billington, Antoniou, Governatori, and Maher—are discussed. (shrink)

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining (...) the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards. (shrink)

Dynamic doxastic logic (DDL) is used in connexion with theories of belief revision. Here we try to show that languages of DDL are suitable also for discussing aspects of default logic. One ingredient of our analysis is a concept of coherence-as-ratifiability.

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics (...) for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours. (shrink)

Temporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate algebraic notions are (...) defined(in a category theoretical manner) and exploited. In particular, thenotion of joint closure is used to construct one model subsuming a setof models. Using this universal algebraic construction we show that aset of linear models can be merged to a unique branching time model.Logical properties of the described algebraic constructions are studied.The proposed approach has been successfully aplied to obtain anappropriate semantics for non-monotonic reasoning processes based ondefault logic. References are discussed that show the details of theseapplications. (shrink)