Rewriting Logic as a Logical and Semantic Framework

Narciso Martí-Oliet and  José Meseguer

Rewriting logic s proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems.

Using concepts from the theory of general logics, representations of an object logic L in a framework logic F are understood as  mappings L -> F that translate one logic into the other in a conservative way.  The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of ``sequent,'' is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L -> RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of L and of RWLogic.  Representation maps of this kind provide executable specifications of the corresponding object logics within rewriting logic, which can be very useful for prototyping purposes.

Regarding the different but related use of rewriting logic as a semantic framework, the straightforward way in which very diverse models of concurrency can be expressed and unified within rewriting logic is emphasized and illustrated with examples such as concurrent object-oriented programming and CCS. The relationship with structural operational semantics is discussed by means of examples. In addition, the way in which constraint solving fits within the rewriting logic framework is briefly explained. Finally, the use of rewriting logic as a logic of change that overcomes the frame problem in AI is also discussed.

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