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A Reinterpretation of the Semilattice Semantics with Applications
In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational...
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Justification Logic and Type Theory as Formalizations of Intuitionistic Propositional Logic
We explore two ways of formalizing Kreisel’s addendum to the Brouwer-Heyting-Kolmogorov interpretation. To do this we compare Artemov’s justification...
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Composition of Deductions within the Propositions-As-Types Paradigm
Kosta Došen argued in his papers Inferential Semantics Došen (in Inferential semantics, Springer, Berlin 2015) and On the Paths of Categories Došen...
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A Joint Logic of Problems and Propositions
AbstractIn a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper On the interpretation of intuitionistic logic ...
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Constructive and Mechanised Meta-Theory of Intuitionistic Epistemic Logic
Artemov and Protopopescu proposed intuitionistic epistemic logic (IEL) to capture an intuitionistic conception of knowledge. By establishing...
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On the Constructive Truth and Falsity in Peano Arithmetic
Recently, Artemov [4] offered the notion of constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its...
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Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant....
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First-Order Intuitionistic Epistemic Logic
Intuitionistic epistemic logic (IEL), introduced by Artemov and Protopopescu (2016), accepts the co-reflection axiom: “...
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Modal Type Theory Based on the Intuitionistic Modal Logic \(\mathbf{IEL}^{-}\)
The modal intuitionistic epistemic logic \(\mathbf{IEL}^{-}\) was proposed by Artemov and Protopopescu as the intuitionistic version of belief logic....
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Undefinability in Inquisitive Logic with Tensor
Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an...
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Introduction:Gödel’s functional interpretation in context
In the spring of 1941, Kurt Gödel held a lecture course on intuitionistic logic at the Institute for Advanced Study in Princeton. Two spiral...
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Structuring Co-constructive Logic for Proofs and Refutations
This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following Trafford...
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Realist Consequence, Epistemic Inference, Computational Correctness
Standard views on logical consequence stem historically from the propositions as truth-bearers tradition on the one hand, and from the assertoric...
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Arithmetization of Logic
Hilbert is not the originator of the expression “metamathematics”, but he is the first to define it as the theory of formal systems designed to...
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Intuitionistic Logic
So far our logics have satisfied the principle of excluded middle (PEM): any statement φ is true or its negation is true, in formula: φ∨¬φ is true....
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Reasoning with Justifications
This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic...
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The Unintended Interpretations of Intuitionistic Logic
We present an overview of the unintended interpretations of intuitionistic logic that arose after Heyting formalized the “observed regularities” in...
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On Two Models of Provability
Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The...