Displaying similar documents to “Integrating intuitionistic and classical theories”

Computational logics and the philosophy of language: the problem of lexical meaning in formal semantics.

Marcello Frixione (1996)

Mathware and Soft Computing

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This paper deals with the possible contributions that logical researches carried on in the field of artificial intelligence (AI) could give to formal theories of meaning developed by logically oriented philosophers of language within the tradition of analytic philosophy. In particular, I will take into account a topic which is problematic in many respects for traditional logical accounts of meaning, i.e., the problem of lexical semantics. My thesis is that AI logics could give useful...

The Axiomatization of Propositional Logic

Mariusz Giero (2016)

Formalized Mathematics

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This article introduces propositional logic as a formal system ([14], [10], [11]). The formulae of the language are as follows φ ::= ⊥ | p | φ → φ. Other connectives are introduced as abbrevations. The notions of model and satisfaction in model are defined. The axioms are all the formulae of the following schemes α ⇒ (β ⇒ α), (α ⇒ (β ⇒ γ)) ⇒ ((α ⇒ β) ⇒ (α ⇒ γ)), (¬β ⇒ ¬α) ⇒ ((¬β ⇒ α) ⇒ β). Modus ponens is the only derivation rule. The soundness theorem and the strong completeness theorem...

On d-finiteness in continuous structures

Itaï Ben Yaacov, Alexander Usvyatsov (2007)

Fundamenta Mathematicae

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We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite"....