Displaying similar documents to “Inference in Action”

Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3

Daishi Yazaki (2019)

Bulletin of the Section of Logic

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The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and S4.3. The application of the inference rules is said to be acceptable, if all the formulas in the upper sequents are subformula of the formulas in lower sequent. For some modal logics, Takano analyzed the relationships between the acceptable inference rules and semantical...

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 Dynamic Epistemic Logic for Actual Knowledge

Arkadiusz Wójcik (2020)

Bulletin of the Section of Logic

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The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the past literature, our system is not burdened with the problem of logical omniscience, that is, an idealized assumption that the agent explicitly knows all classical tautologies and all logical consequences of his or her knowledge. We provide a sound and complete axiomatization...

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...

Propositional Linear Temporal Logic with Initial Validity Semantics1

Mariusz Giero (2015)

Formalized Mathematics

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In the article [10] a formal system for Propositional Linear Temporal Logic (in short LTLB) with normal semantics is introduced. The language of this logic consists of “until” operator in a very strict version. The very strict “until” operator enables to express all other temporal operators. In this article we construct a formal system for LTLB with the initial semantics [12]. Initial semantics means that we define the validity of the formula in a model as satisfaction in the initial...

Logic of existence and logic of knowledge. Epistemic and non epistemic aspects of logic

Michel Bourdeau (2003)

Philosophia Scientiae

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Contrairement à ce qui a parfois été dit, la logique classique et la logique intuitionniste ne s’opposent pas comme une logique de l’existence à une logique de la connaissance. Les considérations épistémologiques trouvent naturellement leur place dans le cadre de la logique classique, sans qu’il soit nécessaire de faire intervenir aucun principe intuitionniste ; il suffit pour cela de reconnaître que la logique ne peut se passer de la notion d’assertion, ou si l’on préfère de jugement....