Search

Religious expressivism is the view that religious sentences, like 'God is all-loving' and 'God offers us the gift of salvation', are devoid of cognitive meaning. Such sentences are not truth-evaluable: they cannot be judged as true or false. In Religious Language , Michael Scott asked what explains the seeming logical behaviour of religious sentences if they are not truth-evaluable, as religious expressivists claim. In particular, religious expressivists need to explain (i) how a given religious sentence and its negation seem inconsistent and (ii) how religious sentences could figure in logically valid arguments. In this article, I develop a version of Weak Kleene semantics that could address these two 'logic' challenges. [ABSTRACT FROM AUTHOR]

This conversation elaborates on the latest work of the Paris-based writer, philosopher, translator, mathematician and pianist Andrei Vieru, where he maintains that human freedom is inseparable from the idea of closure. Vieru’s model is rooted in the topological semantics of modal logic and provides valuable epistemological insights for the broader community of scholars (death and grief scholars, social scientists, humanists) as well as for policymakers, civil social actors and, generally, for all existentially concerned individuals in times of eroding democracies and pressing global risks. In this dialogue conducted during 2023 in face-to-face sessions and via email exchanges between Paris and Bucharest, Vieru reflects on what is at stake philosophically, artistically and existentially when humans are confronted with the radical openness of possibilities brought by contemporary challenges like global crises and digital technologies. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition's truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique value. In this paper we will study which modal logics can be obtained by changing the interpretation of the □ modality, assuming that the interpretation of other connectives stays constant. We will show what axioms are responsible for a particular interpretations of □ . Furthermore, we will study subsets of these axioms. We show that some of the combinations of the axioms are equivalent to well-known modal axioms. We apply the level-valuation technique to all of the systems to regain the closure under the rule of necessitation. We also point out that some of the resulting logics are not sublogics of S5 and comment briefly on the corresponding frame conditions that are forced by these axioms. Ultimately, we sketch a proof of meta-completeness for all of these systems. [ABSTRACT FROM AUTHOR]

The aim of this article is to show that, just as in recent years Cobreros, Egré, Ripley and van Rooij have provided a non-transitive counterpart of classical logic (i.e. one in which all classically acceptable inferences are valid but Cut and other metainferences are not), the same can be done for every Tarskian logic, with full generality. To establish this fact, a semantic approach is taken by showing that appropriate structures can be devised to characterize a non-transitive counterpart of every Tarskian logic, starting from the logical matrices that are usually taken to render them. [ABSTRACT FROM AUTHOR]

Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to align smoothly with program logics used in deductive verification and formal specification of concurrent programs. Our semantics separates local evaluation of expressions and statements performed in an abstract, symbolic environment from their composition into global computations, at which point they are concretised. This makes incremental addition of new language concepts possible, without the need to revise the framework. The basis is a generalisation of the notion of a program trace as a sequence of evolving states that we enrich with event descriptors and trailing continuation markers. This allows to postpone scheduling constraints from the level of local evaluation to the global composition stage, where well-formedness predicates over the event structure declaratively characterise a wide range of concurrency models. We also illustrate how a sound program logic and calculus can be defined for this semantics. [ABSTRACT FROM AUTHOR]

We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this logic enjoys a weak version of the fixed point property. Secondly, we introduce a system of sequent calculus and prove the cut‐elimination theorem for it. As a consequence, we prove that the logic enjoys the Craig interpolation property. Thirdly, we show that the logic is the natural basis of a generalization of simplified Veltman semantics, and prove that it has the finite frame property with respect to that semantics. Finally, we prove that it is sound and complete with respect to some appropriate arithmetical semantics. [ABSTRACT FROM AUTHOR]

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term 'bitstring semantics'!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. [ABSTRACT FROM AUTHOR]

In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson's propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives. [ABSTRACT FROM AUTHOR]

Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if ∧ and ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language. [ABSTRACT FROM AUTHOR]

This study focuses on a factor known to increase sentence processing complexity – negation. We sought to distill out of negation a logical property – Inference Reversal – to see whether it, and not an actual negation word, determines this complexity. First, we tested a negation-less pair of polar operators (at most, at least) in Hebrew. We found that processing time for sentences containing the Inference Reversing at most lagged behind those with at least. Second, we compared the processing of sentences containing two Inference Reversing operators (not less) to sentences with zero (ø, more) and one (not more, less). Since two Inference Reversing Operators annul Inference Reversal ("two negatives make a positive"), we asked whether their processing cost is annulled, or rather cumulative. Surprisingly, RTnot less was shorter than RTnot more. These findings lead to the conclusion that even when covert, Inference Reversal is an important determinant of processing complexity. [ABSTRACT FROM AUTHOR]

Causal models show promise as a foundation for the semantics of counterfactual sentences. However, current approaches face limitations compared to the alternative similarity theory: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This article addresses these difficulties using exogenous interventions, where causal interventions change the values of exogenous variables rather than structural equations. This model accommodates judgments about backtracking counterfactuals, extends to logically complex counterfactuals, and validates familiar principles of counterfactual logic. This combines the interventionist intuitions of the causal approach with the logical advantages of the similarity approach. [ABSTRACT FROM AUTHOR]

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics , which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. [ABSTRACT FROM AUTHOR]

Call a truth complete with respect to a subject matter if it entails every truth about that subject matter. One attractive way to formulate a complete truth is to state all the relevant positive truths, and then add: and that's it. When the subject matters under consideration are non-contingent, a non-trivial conception of completeness must invoke a hyperintensional conception of entailment, and of the completion operation denoted by 'that's it'. This paper develops two complementary hyperintensional conceptions of completion using the framework of truthmaker semantics and determines the resulting logics of totality. [ABSTRACT FROM AUTHOR]

Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is 'semantically laden' and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas that inform her account, and to discuss their significance for the philosophy of logic in general and Frege's philosophy in particular. [ABSTRACT FROM AUTHOR]

According to Schroeder-Heister 2018, proof-theoretic semantics is 'an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth. In this sense proof-theoretic semantics is semantics in terms of proof. Proof-theoretic semantics also means the semantics of proofs, i.e. the semantics of entities which describe how we arrive at certain assertions given certain assumptions.' This text advocates that proof-theoretic semantics, as described above, was an approach to semantical issues in logic that appeared in mainstream philosophical literature at least a couple of centuries before the tradition of general proof theory (cf. Prawitz 1971) came into being. This is done by means of an interpretive analysis of Kant's 1762 essay Die falsche Spitzfindigkeit der vier syllogistischen Figuren, in which two theses are argued: first, that the issue of justifying the logical validity of inferences is approached by Kant in this text, in a strong sense, in terms of proofs; and second, that the purpose of his effort is to establish a point concerning the semantical equivalence between certain distinct valid inferences. [ABSTRACT FROM AUTHOR]

Most ordinary objects - cats, humans, mountains, ships, tables, etc. - have indeterminate mereological boundaries. If the theory of mereology is meant to include ordinary objects at all, we need it to have some space for mereological indeterminacy. In this paper, we present a novel degree-theoretic semantics - Boolean semantics - and argue that it is the best degree-theoretic semantics for modeling mereological indeterminacy, for three main reasons: (a) it allows for incomparable degrees of parthood, (b) it enforces classical logic, and (c) it is compatible with all the axioms of classical mereology. Using Boolean semantics, we will also investigate the connection between vagueness in parthood and vagueness in existence/identity. We show that, contrary to what many have argued, the connection takes neither the form of entailment nor the form of exclusion. [ABSTRACT FROM AUTHOR]

We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus SC2Int for the bi-intuitionistic logic 2Int. A distinctive feature of SC2Int is that it makes use of two kinds of sequents, one representing proofs, the other representing refutations. The structural rules of SC2Int, in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through two different negation connectives, the well-known implies-falsity negation and the less well-known coimplies-truth negation of 2Int. By assuming that the interaction rules have no impact on the identity of derivations, the concept of inherited identity between derivations in SC2Int is introduced and the notions of positive and negative synonymy of formulas are defined. Several examples are given of distinct formulas that are either positively or negatively synonymous. It is conjectured that the two conditions cannot be satisfied simultaneously. [ABSTRACT FROM AUTHOR]

Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment—a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE , one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension—in the sense of Feferman—is as strong as the schematic extension of KF , thus matching the strength of predicative analysis. [ABSTRACT FROM AUTHOR]

This article aims at providing some extension of the modal square of opposition in the light of Ockham's account of modal operators. Moreover, we set forth some significant remarks on the de re–de dicto distinction and on the modal operator of contingency by means of a set-theoretic algebra called numbering semantics. This generalization starting from Ockham's account of modalities will allow us to take into consideration whether Ockham's account holds water or not, and in which case it should be changed. [ABSTRACT FROM AUTHOR]

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, that is, how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation. [ABSTRACT FROM AUTHOR]

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). [ABSTRACT FROM AUTHOR]

Dialogue reasoning is a new task beyond the traditional dialogue system, because it requires recognizing not only semantic relevance but also logical consistency between the candidate response and the dialogue history. Like "all happy families are happy alike, all unhappy families are unhappy in their own way", various illogical patterns exist in the data. For example, some candidate responses use many similar words but with contradicted meanings with history; while some candidates may employ totally different words but convey consistent meanings. Therefore, an ideal dialogue reasoning model should gather clues from both coarse-grained utterance-level and fine-grained word-level to determine the logical relation between candidates and the dialogue history. However, traditional models mainly rely on the widely used BERT to read all the history and candidates word by word but ignore the utterance-level signals, which cannot well capture various illogical patterns in this task. To tackle this problem, we propose a novel Hierarchical BERT (HiBERT) to recognize both utterance-level and word-level illogical patterns in this paper. Specifically, BERT is firstly utilized to encode the dialogue history and each candidate response as the contextualized representation. Secondly, hierarchical reasoning architecture is conducted with this contextualized representation to obtain the word-level and the utterance-level attention distributions, respectively. In detail, we utilize the word-grained attention mechanism to obtain the word-level representation, and propose two different types of attention function, i.e, hard attention and soft attention, to obtain the utterance-grained representation. Finally, we fuse both the word-grained representation and the utterance-grained representation to calculate the logical ranking scores for the given candidate. Experimental results on two public dialogue datasets show that our model obtains higher ranking measures than the widely used BERT model, validating the effectiveness of hierarchical reading of HiBERT. Further analysis on the impact of context length and attention weights shows that the HiBERT actually has the ability to recognize different illogical patterns. [ABSTRACT FROM AUTHOR]

Featherweight Generic Go (FGG) is a minimal core calculus modeling the essential features of the programming language Go. It includes support for overloaded methods, interface types, structural subtyping, and generics. The most straightforward semantic description of the dynamic behavior of FGG programs is to resolve method calls based on runtime type information of the receiver. This article shows a different approach by defining a type-directed translation from ${\textrm{FGG}^{-}}$ to an untyped lambda-calculus. ${\textrm{FGG}^{-}}$ includes all features of FGG but type assertions. The translation of an ${\textrm{FGG}^{-}}$ program provides evidence for the availability of methods as additional dictionary parameters, similar to the dictionary-passing approach known from Haskell type classes. Then, method calls can be resolved by a simple lookup of the method definition in the dictionary. Every program in the image of the translation has the same dynamic semantics as its source ${\textrm{FGG}^{-}}$ program. The proof of this result is based on a syntactic, step-indexed logical relation. The step index ensures a well-founded definition of the relation in the presence of recursive interface types and recursive methods. Although being non-deterministic, the translation is coherent. [ABSTRACT FROM AUTHOR]

Language-of-thought hypothesis (LoTH) is having a profound impact on cognition studies. However, much remains unknown about its basic primitives and generative operations. Infant studies are fundamental, but methodologically very challenging. By distilling potential primitives from work in natural-language semantics, an approach beyond the corset of standard formal logic may be undertaken. Still, the road ahead is challenging and long. [ABSTRACT FROM AUTHOR]

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic) and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of formulas whose top rows differ. [ABSTRACT FROM AUTHOR]

Many analyses of notion of metainferences in the non-transitive logic ST have tackled the question of whether ST can be identified with classical logic. In this paper, we argue that the primary analyses are overly restrictive of the notion of metainference. We offer a more elegant and tractable semantics for the strict-tolerant hierarchy based on the three-valued function for the LP material conditional. This semantics can be shown to easily handle the introduction of mixed inferences, i.e., inferences involving objects belonging to more than one (meta)inferential level and solves several other limitations of the ST hierarchies introduced by Barrio, Pailos, and Szmuc. [ABSTRACT FROM AUTHOR]

G3 is Gödelian 3-valued logic, G3Ł≤ is its paraconsistent counterpart and G3Ł≤ is a strong extension of G3Ł≤. The aim of this paper is to endow each one of the logics just mentioned with a 2 set-up binary Routley semantics. [ABSTRACT FROM AUTHOR]

Epistemic contradictions are now a well-known and often discussed phenomenon among those who study epistemic modals. These contradictions are expressed by sentences like 'It is raining and it might not be raining' whose oddness to the common ear demands an explanation. However, it has turned out to be a rather controversial enterprise to provide such an explanation in a sufficiently precise and general manner. According to pragmatic explanations, epistemic contradictions are semantically consistent but pragmatically defective. According to semantic explanations, one should regard epistemic contradictions as plain semantic inconsistencies. Endorsing such a semantic solution is, however, tantamount to rejecting classical logic, which predicts the consistency of epistemic contradictions. After arguing that all existing solutions to this problem face as yet unmet challenges, I will present a new solution that adequately overcomes these challenges. I will propose to view epistemic contradictions as semantically consistent but epistemically defective sentences. The main thesis emerging will be that we need neither abandon the inference rules of classical logic nor the classical truth-conditional approach to semantics to deal adequately with epistemic contradictions. [ABSTRACT FROM AUTHOR]

Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, and either are or are not about necessary facts. Classical two-dimensionalism has no account of question meanings, so it has to be combined with a framework for question semantics in order to capture these observations. It is shown in [14] how two-dimensional semantics can be combined with inquisitive semantics, in which questions are analyzed in terms of information. The present paper investigates the logic of two-dimensional inquisitive semantics, and provides a complete proof system. [ABSTRACT FROM AUTHOR]

In Minker and Rajasekar (J Log Program 9(1):45–74, 1990), Minker proposed a semantics for negation-free disjunctive logic programs that offers a natural generalisation of the fixed point semantics for definite logic programs. We show that this semantics can be further generalised for disjunctive logic programs with classical negation, in a constructive modal-theoretic framework where rules are built from claims and hypotheses, namely, formulas of the form □ φ and ◊ □ φ where φ is a literal, respectively, yielding a "base semantics" for general disjunctive logic programs. Model-theoretically, this base semantics is expressed in terms of a classical notion of logical consequence. It has a complete proof procedure based on a general form of the cut rule. Usually, alternative semantics of logic programs amount to a particular interpretation of nonclassical negation as "failure to derive." The counterpart in our framework is to complement the original program with a set of hypotheses required to satisfy specific conditions, and apply the base semantics to the resulting set. We demonstrate the approach for the answer set semantics. The proposed framework is purely classical in mainly three ways. First, it uses classical negation as unique form of negation. Second, it advocates the computation of logical consequences rather than of particular models. Third, it makes no reference to a notion of preferred or minimal interpretation. [ABSTRACT FROM AUTHOR]

We demonstrate the first recurrent neural network architecture for learning signal temporal logic (TL) formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not explicitly formalized. There is great interest in learning formal specifications that characterize the ideal behavior of such systems—that is, formulas in TL that are satisfied by the system’s output signals. Such specifications can be used to better understand the system’s behavior and improve the design of its next iteration. Previous inference methods either assumed certain formula templates, or did a heuristic enumeration of all possible templates. This work proposes a neural network architecture that infers the formula structure via gradient descent, eliminating the need for imposing any specific templates. It combines the learning of formula structure and parameters in one optimization. Through systematic comparison, we demonstrate that this method achieves similar or better misclassification rates (MCRs) than enumerative and lattice methods. We also observe that different formulas can achieve similar MCR, empirically demonstrating the under-determinism of the problem of TL inference. [ABSTRACT FROM AUTHOR]

Online monitoring is a popular validation approach in which the temporal behavior of a system is checked to assess whether it satisfies a given specification expressed, e.g., in signal temporal logic (STL). This is done by employing a monitor that, at each time point, states the specification validity: satisfied, violated, or unknown. In some settings, monitoring should continue even after a violation episode is detected, to detect possible future violation episodes. However, for a monitor just relying on STL semantics, this is not possible, as, once the specification is violated by an input signal, any continuation of the signal still violates the specification. To tackle this problem, we here propose an optimal reset technique that, at runtime, detects the end of a violation episode and shifts the evaluation of the monitor to skip such an episode. In this way, the monitoring can continue to detect possible other future violation episodes. We propose a framework that integrates the reset technique with an existing monitoring approach. Experiments on two Simulink models show that the technique can effectively reset the monitor and report all the violation episodes, with a negligible overhead on the monitoring cost. [ABSTRACT FROM AUTHOR]

This paper introduces the logic QLETF, a quantified extension of the logic of evidence and truth LETF, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LETF is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A's violating some classically valid inferences. The semantics of QLETF combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin's method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics. [ABSTRACT FROM AUTHOR]

Belief revision theories standardly endorse a principle of intensionality to the effect that ideal doxastic agents do not discriminate between pieces of information that are equivalent within classical logic. I argue that this principle should be rejected. Its failure, on my view, does not require failures of logical omniscience on the part of the agent, but results from a view of the update as mighty: as encoding what the agent learns might be the case, as well as what must be. The view is motivated by consideration of a puzzle case, obtained by transposing into the context of belief revision a kind of scenario that Kit Fine has used to argue against intensionalism about counterfactuals. Employing the framework of truthmaker semantics, I go on to develop a novel account of belief revision, based on a conception of the update as mighty, which validates natural hyperintensional counterparts of the usual AGM postulates. [ABSTRACT FROM AUTHOR]

This article provides a basic overview of the grammar of conditionals, the role of conditionally in predicate logic, and the difference between conditionally and causality. Medical writers must achieve mastery of these concepts, which are important not just for clear writing but for rational thinking. English speakers use conditionals for many different purposes, such as describing facts, habits, and rules (zero-order conditionals); describing the future consequences of realistic, possible, or likely events (first-order conditionals); expressing the likely consequence of some uncertain or impossible event (second-order conditionals); or talking about how things could have turned out differently if some condition had been met in the past (third-order conditionals). Conditionals also allow one to ask questions about the consequences of an event or to express the conditions under which a command should be followed. Conditional constructions are also sometimes used in expressions that don't really express conditions (relevance conditionals). The grammatical differences between these expressions are subtle, involving the tense and mood of the verbs. Conditionals allow you to talk about how the truth-values of different propositions are interrelated. Thus, once you master the grammar of conditionals, you can begin to learn the rules and pitfalls of deductive and inductive reasoning. In science, such reasoning is often the first step toward proving causality. The existence of a tight correlation between two phenomena does not prove that one causes the other, but the lack of a correlation suggests that a causal relationship is unlikely. [ABSTRACT FROM AUTHOR]

In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these "pure theories of connexive implication"). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of the systems have the variable sharing property). I emphasize the intuitive content of the semantics and discuss how natural informational considerations underly each of the examined systems. [ABSTRACT FROM AUTHOR]

Due to the miscellaneous ambiguity of semantics in open-domain conversation, current deep dialogue models disregard to detect potential emotional and action response features in the latent space, which leads to the general tendency to produce inaccurate and irrelevant sentences. To address this problem, we propose a semantic-aware conditional variational autoencoder that discriminates the sentiment and action responses features in the latent space for one-to-many open-domain dialogue generation. Specifically, explicit controllable variables are leveraged from the proposed module to create diverse conversational texts. This controllable variable can constrain the distribution of the latent space, disentangling the latent space features during training. Furthermore, the feature disentanglement improves the dialogue generation in terms of deep learning interpretability and text quality, which also reveals the latent features of different emotions on the logic of text generation. [ABSTRACT FROM AUTHOR]

The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so‐called full labels and maximal labels. After a general treatment of assuringness, we shall apply it to obtain a completeness result for the modal logic ILP$\mathsf {ILP}$ w.r.t. generalised semantics for a restricted class of frames. [ABSTRACT FROM AUTHOR]

In this article, we address a multi-robot planning problem in environments with partially unknown semantics. The environment is assumed to have a known geometric structure (e.g., walls) and to be occupied by static labeled landmarks with uncertain positions and classes. This modeling approach gives rise to an uncertain semantic map generated by semantic simultaneous localization and mapping algorithms. Our goal is to design control policies for robots equipped with noisy perception systems so that they can accomplish collaborative tasks captured by global temporal logic specifications. To specify missions that account for environmental and perceptual uncertainty, we employ a fragment of linear temporal logic (LTL), called co-safe LTL, defined over perception-based atomic predicates modeling probabilistic satisfaction requirements. The perception-based LTL planning problem gives rise to an optimal control problem, solved by a novel sampling-based algorithm, that generates open-loop control policies that are updated online to adapt to a continuously learned semantic map. We provide extensive experiments to demonstrate the efficiency of the proposed planning architecture. [ABSTRACT FROM AUTHOR]

This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant's 'Critical Philosophy'. Part I reviews some old work of mine that applies these models to provide a reading of Kant's second antinomy about the divisibility of matter and to answer several attacks on Kant's antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant's second antinomy claim that matter is divisible 'ad infinitum' and his first antinomy claim that empirical space extends only 'ad indefinitum'. Secondly, in conformity with the 'assertability' heuristics for Kripke models, it attributes an assertability semantics to Kant. In fact, it attributes a pair of assertability semantics to Kant, but neither of these accords with modern assertabilism. And finally, one must wonder the propriety of using contemporary assertability and contemporary formal logic to save an eighteenth-century text. Part II goes historical to solve the problems about assertability. It outlines the Descartes–Leibniz dialectic about the infinite/indefinite distinction and demonstrates how each position reflects larger philosophical positions. It then demonstrates that Kant's two versions of assertability and his version of the infinite/indefinite dichotomy emerge naturally from his attempts (pre-critical and then critical) to resolve a tension in Leibniz's philosophy. In light of this demonstration, Part III adapts the Kripke model interpretation so that it does reflect that dichotomy. It then refines the Kripke semantics in order to model some of Kant's signature critical doctrines, and it shows how Kant's critical version of the infinite/indefinite distinction differs from all those of his predecessors and from his own pre-critical version. It also addresses the question of using contemporary logical machinery to interpret Kant. Part IV turns the tables and uses what we have learned about Kant and modern semantics in order to address a pair of issues in the contemporary critical foundations of logic. [ABSTRACT FROM AUTHOR]

Critical views of logic are presented. These are views that are critical of logic in a sense akin to the way in which Kant is critical rather than dogmatic about traditional metaphysics. Such approaches differ from the Fregean 'logic-first' view. In accordance with the latter, logic is often regarded as epistemologically and methodologically fundamental. Hence, all disciplines – including mathematics – are considered as answerable to logic, rather than vice versa. In critical views of logic, by contrast, the logical principles that govern some subject matter may depend on the metaphysics of this subject matter or on the semantics of our discourse about it. Space is thereby carved out between a Fregean position on the one hand and thoroughgoing holism à la Quine on the other. [ABSTRACT FROM AUTHOR]

Syllogistic reasoning lies at the intriguing intersection of natural and formal reasoning of language and logic. Syllogisms comprise a formal system of reasoning yet make use of natural language quantifiers (e.g., all, some) and invite natural language conclusions. The conclusions people tend to draw from syllogisms, however, deviate substantially from the purely logical system. Are principles of natural language understanding to blame? We introduce a probabilistic pragmatic perspective on syllogistic reasoning: We decompose reasoning with natural language arguments into two subproblems: language comprehension and language production. We formalize models of these processes within the Rational Speech Act framework and explore the pressures that pragmatic reasoning places on the production of conclusions. We test our models on a recent, large data set of syllogistic reasoning and find that the selection process of conclusions from syllogisms are best modeled as a pragmatic speaker who has the goal of aligning the beliefs of a naive listener with those of their own. We compare our model to previously published models that implement two alternative theories—Mental Models and Probability Heuristics—finding that our model quantitatively predicts the full distributions of responses as well as or better than previous accounts, but with far fewer parameters. Our results suggest that human syllogistic reasoning may be best understood not as a poor approximation to ideal logical reasoning, but rather as rational probabilistic inference in support of natural communication. People often face reasoning problems with assumptions and conclusions stated in natural language, suggesting that pragmatic factors of human language use will affect reasoning. We develop a probabilistic pragmatics model for the comprehension of argument premises and production of conclusions. This model explains data from syllogistic reasoning experiments, suggesting that some features of "illogical reasoning" are in fact rational probabilistic inferences in support of natural communication. [ABSTRACT FROM AUTHOR]

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly as in Andersonian-Kangerian reduction, which uses different intensional implications and constants. [ABSTRACT FROM AUTHOR]

For each n ∈ N , we introduce the algebraic semantics for the minimum many-valued modal logic over the MV-chain with n elements. We prove that this quasivariety of algebras is generated by the complex algebras, obtaining as a consequence the completeness result of the logic with respect to the Kripke semantics. As a first step towards the study of this algebraic semantics, we study some congruences of the complex algebras. [ABSTRACT FROM AUTHOR]

In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent calculi are constructed based on a falsification-aware setting for first-order Nelson constructive three-valued logic (N3). In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3 (i.e., a classical variant of N3 is identical to first-order classical logic). The completeness and cut-elimination theorems for the proposed semantics and sequent calculi are proved using Schütte's method. Similar results for the propositional case are also obtained. [ABSTRACT FROM AUTHOR]

This work presents a proof-theoretical and model-theoretical approach to probabilistic temporal logic. We present two novel logics; each of them extends both the language of linear time logic (LTL) and the language of probabilistic logic with polynomial weight formulas. The first logic is designed for reasoning about probabilities of temporal events, allowing statements like "the probability that A will hold in next moment is at least the probability that B will always hold" and conditional probability statements like "probability that A will always hold, given that B holds, is at least one half", where A and B are arbitrary statements. We axiomatize this logic, provide corresponding sigma additive semantics and prove that the axiomatization is sound and strongly complete. We show that the satisfiability problem for our logic is decidable, by presenting a procedure which runs in polynomial space. We also present a logic with much richer language, in which probabilities are not attached only to temporal events, but the language allows arbitrary nesting of probability and temporal operators, allowing statements like "probability that tomorrow the chance of rain will be less than 80% is at least a half". For this logic we prove a decidability result. [ABSTRACT FROM AUTHOR]

This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (Journal of Philosophical Logic, 4545, 199–226 13, 14, 15) introduces. I will then move to compare the resulting logic of propositional identity (PI1) with Correia's (The Review of Symbolic Logic, 9, 103–122 9) logic of generalised identity (GI), as well as the first degree fragment of Angell's (2) logic of analytic containment (AC). The paper concludes by extending PI1 to include axioms and rules for a subject-matter operator, providing a much broader theory of subject-matter than the principles with which I will begin. [ABSTRACT FROM AUTHOR]

In this article, we present an approach based on counterexample-guided abstraction refinement to verifying full regular temporal properties of C programs by means of combining both static analysis and dynamic verification. To this end, a desired property is specified by a propositional projection temporal logic formula $p$ , and the labeled normal form graph (LNFG) of $\lnot p$ is automatically produced. Furthermore, the control flow automaton of the C program is constructed, and an enriched abstract reachability tree is generated under the guidance of the LNFG. Throughout the construction of the eART, whenever a candidate counterexample $cp$ is found, a verification input w.r.t $cp$ is generated by the SMT solver Z3. Subsequently, the C program is converted into a modeling, simulation, and verification language (MSVL) program $m$ , and $\lnot p$ is also transformed to an MSVL program $m^{\prime }$. As a result, $m\; \text{and} \;m^{\prime }$ is executed to check whether the counterexample is spurious. The $cp$ is returned if it is a real counterexample; otherwise, the eART is refined. This process is repeated until no counterexample is found, namely the property is valid, or the counterexample is a real one The proposed approach enables us to not only verify full regular properties of C programs, but also produce precise results, neither false negatives nor false positives. The approach has been implemented in a tool named SDMC. Experiments show that SDMC outperforms the relevant tools available. [ABSTRACT FROM AUTHOR]

In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot accept her own definition of validity because it is given in a classical meta-theory. It is often suggested that this mismatch between the consequence relation of the account being espoused and the consequence relation of the meta-theory is a serious embarrassment. The main goal of the paper is to explore whether certain substructural accounts of the paradoxes can avoid this sort of embarrassment. Typically, these accounts are expressively incomplete, since they cannot assert in the object language that certain invalid arguments are in fact invalid. To overcome this difficulty I develop a novel type of hybrid proof-procedure, one that takes invalidities to be just as fundamental as validities. I prove that this proof-procedure enjoys a number of interesting properties and I analyze the prospects of applying it to languages capable of expressing self-referential statements. [ABSTRACT FROM AUTHOR]

Prawitz (1971) conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister (2019). This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. [ABSTRACT FROM AUTHOR]