The Modal Logic of Inequality

We consider some modal languages with a modal operator D whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at. ?

[1]  Dag Westerstaåhl,et al.  Quantifiers in Formal and Natural Languages , 1989 .

[2]  Ron Koymans,et al.  Specifying Message Passing and Time-Critical Systems with Temporal Logic , 1992, Lecture Notes in Computer Science.

[3]  Valentin Goranko,et al.  Modal Definability in Enriched Languages , 1989, Notre Dame J. Formal Log..

[4]  J.F.A.K. van Benthem,et al.  Modal logic and classical logic , 1983 .

[5]  Patrick Blackburn.  Nominal tense logic and other sorted intensional frameworks , 1990 .

[6]  Tinko Tinchev,et al.  Modal Environment for Boolean Speculations , 1987 .

[7]  Valentin Goranko,et al.  Modal logic with names , 1993, J. Philos. Log..

[8]  Johan van Benthem,et al.  Notes on Modal Definability , 1988, Notre Dame J. Formal Log..

[9]  D. Gabbay.  An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames , 1981 .

[10]  Wilhelm Ackermann,et al.  Solvable Cases Of The Decision Problem , 1954 .

[11]  Steven K. Thomason,et al.  Semantic analysis of tense logics , 1972, Journal of Symbolic Logic.

[12]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[13]  Johan van Benthem,et al.  The Logic of Time , 1983 .

[14]  Valentin Goranko,et al.  Using the Universal Modality: Gains and Questions , 1992, J. Log. Comput..

[15]  Bruce M. Kapron,et al.  Modal sequents and definability , 1987, Journal of Symbolic Logic.

[16]  S. K. Thomason,et al.  AXIOMATIC CLASSES IN PROPOSITIONAL MODAL LOGIC , 1975 .

[17]  Henrik Sahlqvist.  Completeness and Correspondence in the First and Second Order Semantics for Modal Logic , 1975 .