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  1.  6
    Referentiality and Configurationality in the Idiom and the Phrasal Verb.Cem Bozşahin - 2023 - Journal of Logic, Language and Information 32 (2):175-207.
    Two positions of Bolinger, about synonymy and meaningfulness of words, point to significance of controlling the referentiality of word forms, from representing them in grammar to their projection onto surface structure, i.e. configurationality. In particular, it becomes critical to control the range of surface substitution for surface syntactic categories of words to maintain referential properties of idiosyncrasy. Categorial grammars as reference systems suggest ways to keep the two aspects in grammar. The first dividend of adopting a categorial perspective is systematically (...)
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  2.  4
    Some Notes on Dyadic Contingency.Jie Fan - 2023 - Journal of Logic, Language and Information 32 (2):209-217.
    In a recent work, Pizzi proposes a notion of dyadic non-contingency, and then gives an axiomatic system of dyadic non-contingency named \(\text {KD}\Delta ^2\), which is shown to be translationally equivalent to the deontic system KD and has the minimal system \(\text {K}\Delta \) of monadic contingency as a fragment. However, the reason why he defines dyadic non-contingency like that is unclear. In this article, inspired by the notion of relativized knowing-value in the literature, we give a plausible explanation for (...)
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  3.  5
    Algebraic Effects for Extensible Dynamic Semantics.Julian Grove & Jean-Philippe Bernardy - 2023 - Journal of Logic, Language and Information 32 (2):219-245.
    Research in dynamic semantics has made strides by studying various aspects of discourse in terms of computational effect systems, for example, monads (Shan, 2002; Charlow, 2014), Barker and 2014), (Maršik, 2016). We provide a system, based on graded monads, that synthesizes insights from these programs by formalizing individual discourse phenomena in terms of separate effects, or grades. Included are effects for introducing and retrieving discourse referents, non-determinism for indefiniteness, and generalized quantifier meanings. We formalize the behavior of individual effects, as (...)
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  4.  3
    Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.
    The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...)
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  5.  9
    Type Polymorphism, Natural Language Semantics, and TIL.Ivo Pezlar - 2023 - Journal of Logic, Language and Information 32 (2):275-295.
    Transparent intensional logic (TIL) is a well-explored type-theoretical framework for semantics of natural language. However, its treatment of polymorphic functions, which are essential for the analysis of various natural language phenomena, is still underdeveloped. In this paper, we address this issue and propose an extension of TIL that introduces polymorphism via type variables ranging over types and generalized variables ranging over constructions and types. Furthermore, we offer an analysis of sentences involving non-specific notional attitudes of the general form ‘_A_ considers (...)
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  6.  6
    A Substructural Approach to Explicit Modal Logic.Shawn Standefer - 2023 - Journal of Logic, Language and Information 32 (2):333–362.
    In this paper, we build on earlier work by Standefer (Logic J IGPL 27(4):543–569, 2019) in investigating extensions of substructural logics, particularly relevant logics, with the machinery of justification logics. We strengthen a negative result from the earlier work showing a limitation with the canonical model method of proving completeness. We then show how to enrich the language with an additional operator for implicit commitment to circumvent these problems. We then extend the logics with axioms for D, 4, and 5, (...)
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  7.  6
    Computable Heyting Algebras with Distinguished Atoms and Coatoms.Nikolay Bazhenov - 2023 - Journal of Logic, Language and Information 32 (1):3-18.
    The paper studies Heyting algebras within the framework of computable structure theory. We prove that the class _K_ containing all Heyting algebras with distinguished atoms and coatoms is complete in the sense of the work of Hirschfeldt et al. (Ann Pure Appl Logic 115(1-3):71-113, 2002). This shows that the class _K_ is rich from the computability-theoretic point of view: for example, every possible degree spectrum can be realized by a countable structure from _K_. In addition, there is no simple syntactic (...)
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  8.  6
    On the (Complete) Reasons Behind Decisions.Adnan Darwiche & Auguste Hirth - 2023 - Journal of Logic, Language and Information 32 (1):63-88.
    Recent work has shown that the input-output behavior of some common machine learning classifiers can be captured in symbolic form, allowing one to reason about the behavior of these classifiers using symbolic techniques. This includes explaining decisions, measuring robustness, and proving formal properties of machine learning classifiers by reasoning about the corresponding symbolic classifiers. In this work, we present a theory for unveiling the _reasons_ behind the decisions made by Boolean classifiers and study some of its theoretical and practical implications. (...)
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  9.  4
    Preface.Sujata Ghosh & R. Ramanujam - 2023 - Journal of Logic, Language and Information 32 (1):1-2.
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  10.  4
    Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems.Prosenjit Howlader & Mohua Banerjee - 2023 - Journal of Logic, Language and Information 32 (1):117-146.
    The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. (...)
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  11.  5
    Feferman–Vaught Decompositions for Prefix Classes of First Order Logic.Abhisekh Sankaran - 2023 - Journal of Logic, Language and Information 32 (1):147-174.
    The Feferman–Vaught theorem provides a way of evaluating a first order sentence \(\varphi \) on a disjoint union of structures by producing a decomposition of \(\varphi \) into sentences which can be evaluated on the individual structures and the results of these evaluations combined using a propositional formula. This decomposition can in general be non-elementarily larger than \(\varphi \). We introduce a “tree” generalization of the prenex normal form (PNF) for first order sentences, and show that for an input sentence (...)
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  12.  5
    Deontic Paradoxes in Mīmāṃsā Logics: There and Back Again.Kees van Berkel, Agata Ciabattoni, Elisa Freschi, Francesca Gulisano & Maya Olszewski - 2023 - Journal of Logic, Language and Information 32 (1):19-62.
    Centered around the analysis of the prescriptive portion of the Vedas, the Sanskrit philosophical school of Mīmāṃsā provides a treasure trove of normative investigations. We focus on the leading Mīmāṃsā authors Prabhākara, Kumārila and Maṇḍana, and discuss three modal logics that formalize their deontic theories. In the first part of this paper, we use logic to analyze, compare and clarify the various solutions to the _śyena_ controversy, a two-thousand-year-old problem arising from seemingly conflicting commands in the Vedas. In the second (...)
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