Displaying similar documents to “Barwise Completeness Theorems For Logics With Integrals”

On d-finiteness in continuous structures

Itaï Ben Yaacov, Alexander Usvyatsov (2007)

Fundamenta Mathematicae

Similarity:

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"....

The Axiomatization of Propositional Logic

Mariusz Giero (2016)

Formalized Mathematics

Similarity:

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...

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

Similarity:

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...

Inference in Action

Johan van Benthem (2007)

Publications de l'Institut Mathématique

Similarity: