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Categorial inference and modal logic

Natasha Kurtonina

Journal of Logic, Language and Information 7 (4):399-411 (1998)

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Inter-model connectives and substructural logics.Igor Sedlár - 2014 - In Roberto Ciuni, Heinrich Wansing & Caroline Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Cham, Switzerland: Springer. pp. 195-209.details The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) Download Export citation Bookmark 1 citation
From positive PDL to its non-classical extensions.Igor Sedlár & Vít Punčochář - 2019 - Logic Journal of the IGPL 27 (4):522-542.details We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic. The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residuated operators of the non-associative Lambek calculus. Informal interpretations of these two extensions are outlined. Download Export citation Bookmark 3 citations
Simulating polyadic modal logics by monadic ones.George Goguadze, Carla Piazza & Yde Venema - 2003 - Journal of Symbolic Logic 68 (2):419-462.details We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic $\Lambda^{sim}$ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability. Download Export citation Bookmark 4 citations
A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Cham, Switzerland: Springer International Publishing. pp. 289-337.details This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) Download Export citation Bookmark 2 citations
Algorithmic correspondence and canonicity for distributive modal logic.Willem Conradie & Alessandra Palmigiano - 2012 - Annals of Pure and Applied Logic 163 (3):338-376.details Download Export citation Bookmark 19 citations

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