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  1.  2
    A Computational Treatment of Anaphora and Its Algorithmic Implementation.Jean-Philippe Bernardy, Stergios Chatzikyriakidis & Aleksandre Maskharashvili - 2021 - Journal of Logic, Language and Information 30 (1):1-29.
    In this paper, we propose a framework capable of dealing with anaphora and ellipsis which is both general and algorithmic. This generality is ensured by the compination of two general ideas. First, we use a dynamic semantics which reperent effects using a monad structure. Second we treat scopes flexibly, extending them as needed. We additionally implement this framework as an algorithm which translates abstract syntax to logical formulas. We argue that this framework can provide a unified account of a large (...)
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  2.  1
    Correction to: The Multiplicative-Additive Lambek Calculus with Subexponential and Bracket Modalities.Max Kanovich, Stepan Kuznetsov & Andre Scedrov - 2021 - Journal of Logic, Language and Information 30 (1):89-89.
    In the original publication, the affiliation of the author Max Kanovich was processed incorrectly. It has been updated in this correction.
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  3.  3
    The Multiplicative-Additive Lambek Calculus with Subexponential and Bracket Modalities.Max Kanovich, Stepan Kuznetsov & Andre Scedrov - 2021 - Journal of Logic, Language and Information 30 (1):31-88.
    We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative connectives, additive conjunction and disjunction, brackets and bracket modalities, and the! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut. We also prove algorithmic undecidability for both (...)
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  4.  5
    Inquisitive Propositional Dynamic Logic.Vít Punčochář & Igor Sedlár - 2021 - Journal of Logic, Language and Information 30 (1):91-116.
    This paper combines propositional dynamic logic ) with propositional inquisitive logic ). The result of this combination is a logical system \ that conservatively extends both \ and \, and, moreover, allows for an interaction of the question-forming operator from \ with the structured modalities from \. We study this system from a semantic as well as a syntactic point of view. These two perspectives are linked via a completeness proof, which also shows that \ is decidable.
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  5.  12
    A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3DH.Gemma Robles & José M. Méndez - 2021 - Journal of Logic, Language and Information 30 (1):117-138.
    The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic BM with a dual intuitionistic negation of the type Sylvan defined for the extension CCω of da Costa’s paraconsistent logic Cω. We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3DH, the expansion of G3+ with a dual intuitionistic negation of the kind considered by Sylvan (G3+ is the positive fragment of Gödelian (...)
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  6.  10
    Subatomic Negation.Bartosz Więckowski - 2021 - Journal of Logic, Language and Information 30 (1):207-262.
    The operators of first-order logic, including negation, operate on whole formulae. This makes it unsuitable as a tool for the formal analysis of reasoning with non-sentential forms of negation such as predicate term negation. We extend its language with negation operators whose scope is more narrow than an atomic formula. Exploiting the usefulness of subatomic proof-theoretic considerations for the study of subatomic inferential structure, we define intuitionistic subatomic natural deduction systems which have several subatomic operators and an additional operator for (...)
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  7.  2
    Reasoning with Ambiguity.Christian Wurm - 2021 - Journal of Logic, Language and Information 30 (1):139-206.
    We treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it is no less obvious that ambiguous propositions entail other propositions, and are entailed by other propositions. This article gives a formal analysis of the underlying mechanisms, both from an algebraic and a logical point of view. The main result can be summarized as follows: sound reasoning with ambiguity requires a distinction between equivalence on the one and congruence on the other side: the (...)
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