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We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego’s Theorem. The key ingredients of our proof include the coloring technique and construction of universal models from modal logic. For this we develop duality theory for finite nuclear implicat...
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We prove that the modal logic of a crowded locally compact generalized ordered space is S4. This provides a version of the McKinsey-Tarski theorem for generalized ordered spaces. We then utilize this theorem to axiomatize the modal logic of an arbitrary locally
compact generalized ordered space.
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This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms and dependence quantifiers, modeled within the setting of generalized assignment semantics for FOL. The logic's expressive strength, complete pro...
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This paper studies the relation between persuasive argumentation and the speaker’s epistemic attitude. Dung-style abstract argumentation and dynamic epistemic logic provide the necessary tools to characterize the notion of persuasion. Within abstract argumentation, persuasive argumentation has be...
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. Instantial Neighbourhood Logic (INL) has been introduced
recently as a language for neighbourhood frames where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. Apart from its semantics, its proof theory and bisimulation games have also...
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We apply the technique of filtration to prove completeness for a class of axiomatic extensions of modal logic with the master modality. It suffices that the set of additional axioms is basic modal, canonical and admits filtration. We also take some steps towards generalising our results to sets o...
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This article provides an algebraic study of the propositional system InqB of inquisitive logic. We also investigate the wider class of DNA-logics, which are negative variants of intermediate logics, and the corresponding algebraic structures, DNA-varieties. We prove that the lattice of DNA-logics...
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The celebrated van Benthem characterisation theorem states that on Kripke structures modal logic is the bisimulation-invariant fragment of first-order logic. In this paper we prove an analogue of the van Benthem characterisation theorem for models based on descriptive general frames. This is an i...
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We discuss some of Jankov’s contributions to the study of intermediate logics, including the development of what have become known as Jankov formulas and a proof that there are
continuum many intermediate logics. We also discuss how to generalize Jankov’s technique to
develop axiomatization met...
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Bagaria and V\"a\"an\"anen developed a framework for studying the large cardinal strength of \emph{downwards} L\"owenheim-Skolem theorems and related set theoretic reflection properties. The main tool was the notion of \emph{symbiosis}, originally introduced by the third author.
Symbiosis prov...
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Monotonicity-based inference is a fundamental notion in the logical semantics of natural language, and also in logic in general. Start- ing in generalized quantifier theory, we distinguish three senses of the notion, study their relations, and use these to connect monotonicity to logics of model ...