Journal of Logic Language and Information最新文献

Contrary to what seems to be predicted by a Strawson-inspired view, in presupposition denials the presupposition triggered by, e.g., ‘the king of France’ seems to be cancelled. To explain this puzzling instance of the projection problem, defenders of a Strawson-inspired view have proposed various ad hoc ambiguities. I develop a version of Segmented Discourse Representation Theory that explains the puzzling presupposition-cancelling phenomenon relying only on independently motivated pragmatic processes. Appealing to Kripke’s “test” for the adequacy of ambiguity motivating counterexamples, I argue that my analysis is to be preferred over proposals that posit ad hoc ambiguities. Two key insights of my analysis are, first, that the “cancellation” of presuppositions in presupposition denials depends upon the illocutionary effects of rejection and correction, and, second, that the process of presupposition accommodation often involves the speaker performing an ancillary sort of speech act, viz. the speech act of presupposing.

Arithmetical texts involving division are governed by conventions that avoid the risk of problems to do with division by zero (DbZ). A model for elementary arithmetic texts is given, and with the help of many examples and counter examples a partial description of what may be called traditional conventions on DbZ is explored. We introduce the informal notions of legal and illegal texts to analyse these conventions. First, we show that the legality of a text is algorithmically undecidable. As a consequence, we know that there is no simple sound and complete set of guidelines to determine unambiguously how DbZ is to be avoided. We argue that these observations call for further explorations of mathematical conventions. We propose a method using logics to progress the analysis of legality versus illegality: arithmetical texts in a model can be transformed into logical formulae over special total algebras that are able to approximate partiality but in a total world. The algebras we use are called common meadows. Our dive into informal mathematical practice using formal methods opens up questions about DbZ which we address in conclusion.

This paper is about sentences of form To be human is to be an animal, To live is to fight, etc. I call them ‘infinitive sentences’. I define an augmented propositional language able to express them and give a matrix-based semantics for it. I also give a tableau proof system, called IL for Infinitive Logic. I prove soundness, completeness and a few basic theorems.

Term Functor Logic is a term logic that recovers some important features of the traditional, Aristotelian logic; however, it turns out that it does not preserve all of the Aristotelian properties a valid inference should have insofar as the class of theorems of Term Functor Logic includes some inferences that may be considered irrelevant (e.g. ex falso, verum ad, and petitio principii). By following an Aristotelian or syllogistic notion of relevance, in this contribution we adapt a tableaux method for Term Functor Logic in order to avoid irrelevance and we offer some sort of intuitive semantics in terms of traditional inferential situations (e.g. propter quid, quia, non causa ut causa, and non sequitur).

In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.

A unified and modular falsification-aware single-succedent Gentzen-style framework is introduced for classical, paradefinite, paraconsistent, and paracomplete logics. This framework is composed of two special inference rules, referred to as the rules of explosion and excluded middle, which correspond to the principle of explosion and the law of excluded middle, respectively. Similar to the cut rule in Gentzen’s LK for classical logic, these rules are admissible in cut-free LK. A falsification-aware single-succedent Gentzen-style sequent calculus fsCL for classical logic is formalized based on the proposed framework. The calculus fsCL is obtained from the existing falsification-aware single-succedent Gentzen-style sequent calculus GN4 for Nelson’s paradefinite (or paraconsistent) four-valued logic N4 by adding the rules of explosion and excluded middle. A falsification-aware single-succedent Gentzen-style sequent calculus GN3 for Nelson’s paracomplete three-valued logic N3 is also obtained from GN4 by adding the rule of explosion. The cut-elimination theorems for fsCL, GN3, and some of their neighbors as well as the Glivenko theorem for fsCL are proved.

We describe the foundations and the systematization of natural logic-like monotonic inference using unscoped episodic logical forms (ULFs) that as reported by Kim et al. (Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA), Groningen, 2021a, b) introduced and first evaluated. In addition to providing a more detailed explanation of the theory and system, we present results from extending the inference manager to address a few of the limitations that as reported by Kim et al. (Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA), Groningen, 2021b) naive system has. Namely, we add mechanisms to incorporate lexical information from the hypothesis (or goal) sentence, enable the inference manager to consider multiple possible scopings for a single sentence, and match against the goal using English rather than the ULF.

Transformer-based Pre-Trained Language Models currently dominate the field of Natural Language Inference (NLI). We first survey existing NLI datasets, and we systematize them according to the different kinds of logical inferences that are being distinguished. This shows two gaps in the current dataset landscape, which we propose to address with one dataset that has been developed in argumentative writing research as well as a new one building on syllogistic logic. Throughout, we also explore the promises of ChatGPT. Our results show that our new datasets do pose a challenge to existing methods and models, including ChatGPT, and that tackling this challenge via fine-tuning yields only partly satisfactory results.

The recent advance of large language models (LLMs) demonstrates that these large-scale foundation models achieve remarkable capabilities across a wide range of language tasks and domains. The success of the statistical learning approach challenges our understanding of traditional symbolic and logical reasoning. The first part of this paper summarizes several works concerning the progress of monotonicity reasoning through neural networks and deep learning. We demonstrate different methods for solving the monotonicity reasoning task using neural and symbolic approaches and also discuss their advantages and limitations. The second part of this paper focuses on analyzing the capability of large-scale general-purpose language models to reason with monotonicity.

Many problems in Multi-Agent Systems (MASs) research are formulated in terms of the abilities of a coalition of agents. Existing approaches to reasoning about coalitional ability are usually focused on games or transition systems, which are described in terms of states and actions. Such approaches however often neglect a key feature of multi-agent systems, namely that the actions of the agents require resources. In this paper, we describe a logic for reasoning about coalitional ability under resource constraints in the probabilistic setting. We extend Resource-bounded Alternating-time Temporal Logic (RB-ATL) with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic resource-bounded ATL (pRB-ATL). We implement model-checking algorithms and present experimental results using simple multi-agent model-checking problems of increasing complexity.