The completeness of monotonic modal logics

✍ Scribed by Brian F. Chellas; Audrey McKinney

• Publisher: John Wiley and Sons
• Year: 1975
• Tongue: English
• Weight: 379 KB
• Volume: 21
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19750210150

✦ Synopsis

The purpose of this paper is to point out an error in KRISTER SEGERBERG'S proof of the completeness of the modal logic R, and to provide a correct proof.2) The correct proofbased on a notion and a strategy suggested by SEOERBERO'S techniquesintroduces a general approach for obtaining completeness theorems for modal logics of a kind we call monotonic. I n the main we follow SEGERBERG in terminology and notation. The f i r d two sections review some of the basic concepts relevant to the theorems in the t'hird. *) [2], pp. 42-43. The modal logic H is called ER by SEOERBERQ. s, S m E R B E R Q ' s term for maximal L-consistency. A set of formules is L-maximal if and only if critically on the final draft of this paper. it is L-consistent and has only L-inconsistent extensions ([2], pp. 10-11). ') The lemma is remarked by SEGERBERO ([2], p. 45) and proved (in effect) by GABBAY ([l], p. 6).