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View all- Farahmand Parsa AGhari M(2023)On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of ProofsStudia Logica10.1007/s11225-022-10033-2111:4(573-613)Online publication date: 1-Aug-2023
A Note on Strong Axiomatization of Gödel Justification Logic
Abstract
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators “t : ”, indexed over t by a corresponding set of justification terms, which thus explicitly encode the justification for the necessity assertion in the syntax. With these operators, one can therefore not only reason about modal effects on propositions but also about dynamics inside the justifications themselves. We replace this classical boolean base with Gödel logic, one of the three most prominent fuzzy logics, i.e. special instances of many-valued logics, taking values in the unit interval [0, 1], which are intended to model inference under vagueness. We extend the canonical possible-world semantics for justification logic to this fuzzy realm by considering fuzzy accessibility- and evaluation-functions evaluated over the minimum t-norm and establish strong completeness theorems for various fuzzy analogies of prominent extensions for basic justification logic.
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Published: 01 August 2020
Received: 18 October 2018
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View all- Farahmand Parsa AGhari M(2023)On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of ProofsStudia Logica10.1007/s11225-022-10033-2111:4(573-613)Online publication date: 1-Aug-2023
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