Skip to main content

A Shared Framework for Consequence Operations and Abstract Model Theory

Wallmann, Christian (2013) A Shared Framework for Consequence Operations and Abstract Model Theory. Logica Universalis, 7 (2). pp. 125-145. ISSN 1661-8297. E-ISSN 1661-8300. (doi:10.1007/s11787-012-0069-2) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://doi.org/10.1007/s11787-012-0069-2

Abstract

In this paper we develop an abstract theory of adequacy. In the same way as the theory of consequence operations is a general theory of logic, this theory of adequacy is a general theory of the interactions and connections between consequence operations and its sound and complete semantics. Addition of axioms for the connectives of propositional logic to the basic axioms of consequence operations yields a unifying framework for different systems of classical propositional logic. We present an abstract model-theoretical semantics based on model mappings and theory mappings. Between the classes of models and theories, i.e., the set of sentences verified by a model, it obtains a connection that is well-known within algebra as Galois correspondence. Many basic semantical properties can be derived from this observation. A sentence A is a semantical consequence of T if every model of T is also a model of A. A model mapping is adequate for a consequence operation if its semantical inference operation is identical with the consequence operation. We study how properties of an adequate model mapping reflect the properties of the consequence operation and vice versa. In particular, we show how every concept of the theory of consequence operations can be formulated semantically.

Item Type: Article
DOI/Identification number: 10.1007/s11787-012-0069-2
Uncontrolled keywords: Primary 03C95, Secondary 03B22, Consequence operation, abstract model theory, Galois correspondence, completeness, adequacy, classiacl propositional logic
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
B Philosophy. Psychology. Religion > BC Logic
Divisions: Faculties > Humanities > School of European Culture and Languages > Philosophy
Depositing User: Fiona Godfrey
Date Deposited: 29 Jul 2015 16:01 UTC
Last Modified: 29 May 2019 14:57 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/49893 (The current URI for this page, for reference purposes)
  • Depositors only (login required):