Why Combine Logics?

Combining logics has become a rapidly expanding entreprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages.By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard languages often miss the point. Using the history of quantified modal logic as our main example, we also show that the use of combined structures and logics is a recurring theme in the analysis of existing logical systems.

[1]  Richard Routley,et al.  The Semantics of Entailment. , 1977 .

[2]  Edith Hemaspaandra.  Complexity transfer for modal logic , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[3]  Richard Sylvan,et al.  The semantics of entailment—II , 1972, Journal of Philosophical Logic.

[4]  M. de Rijke,et al.  Zooming In, Zooming Out , 1997, J. Log. Lang. Inf..

[5]  James W. Garson,et al.  Quantification in Modal Logic , 1984 .

[6]  Robert K. Meyer,et al.  Semantics of Entailment 0 , 1993 .

[7]  Wiebe van der Hoek,et al.  First steps in modal logic , 1997 .

[8]  R. Labrecque.  The Correspondence Theory , 1978 .

[9]  M. de Rijke,et al.  A Proof System for Finite Trees , 1995, CSL.

[10]  R. Muskens.  Meaning and Partiality , 1995 .

[11]  Dov M. Gabbay,et al.  Combining Temporal Logic Systems , 1996, Notre Dame J. Formal Log..

[12]  Albert Visser,et al.  Dynamic Bracketing and Discourse Representation , 1996, Notre Dame J. Formal Log..

[13]  Valentin B. Shehtman,et al.  Semantics of Non-Classical First Order Predicate Logics , 1990 .

[14]  Rudolf Carnap,et al.  Meaning and Necessity , 1947 .

[15]  M. de Rijke,et al.  Diamonds and Defaults , 1993 .

[16]  Marcus Kracht,et al.  Properties of independently axiomatizable bimodal logics , 1991, Journal of Symbolic Logic.

[17]  Edith Hemaspaandra,et al.  The Price of Universality , 1996, Notre Dame J. Formal Log..

[18]  Tomek Strzalkowski,et al.  From Discourse to Logic , 1991 .

[19]  Jerry Seligman.  Perspectives: a relativistic approach to the theory of information , 1991 .

[20]  Jeroen Groenendijk,et al.  Dynamic predicate logic , 1991 .

[21]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[22]  Claire Gardent,et al.  A Specification Language for Lexical Functional Grammars , 1995, EACL.

[23]  A. E. Eiben,et al.  Combining Algebraizable Logics , 1996, Notre Dame J. Formal Log..

[24]  Frank Wolter,et al.  A Counterexample in Tense Logic , 1996, Notre Dame J. Formal Log..

[25]  Dov M. Gabbay,et al.  Adding a temporal dimension to a logic system , 1992, J. Log. Lang. Inf..

[26]  Silvio Ghilardi,et al.  Incompleteness results in Kripke semantics , 1991, Journal of Symbolic Logic.