A modal logic amalgam of classical and intuitionistic propositional logic
نویسندگان
چکیده
منابع مشابه
A modal logic amalgam of classical and intuitionistic propositional logic
We present a modal extension of classical propositional logic in which intuitionistic propositional logic is mirrored by means of the modal operator. In this sense, the modal extension combines classical and intuitionistic propositional logic avoiding the collapsing problem. Adopting ideas from a recent paper (S. Lewitzka, A denotational semantics for a Lewis-style modal system close to S1, 201...
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Let `c and `i denote derivability in classical and intuitionistic propositional logic, respectively. Then it is known that if `c A, then ΠV(A) `i A, where V(A) is the set of propositional variables in a formula A and ΠV = {p ∨ ¬p | p ∈ V } for a set V of propositional variables; see, for example, [1], and [4, p. 27] which was originally given in [5]. In this talk, we consider a problem: what se...
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Logic L was introduced by Lewitzka [8] as a modal system that combines intuitionistic and classical logic: L is a conservative extension of CPC and it contains a copy of IPC via embedding φ 7→ φ. In this article, we consider L3, i.e. L augmented with S3 modal axioms, define basic epistemic extensions and prove completeness w.r.t. algebraic semantics. Our systems involve, in adapted form, some o...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2015
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exv048