Review by Choice Review
Where classical logic captures the relations between absolutely true propositions, various modal logics model the relations between propositions that we believe, know, or can prove. The statements in justification logics, a rather new subject, express not only propositions but also our reasons for them in their particular stated form. It could happen that, not seeing the logical equivalence of two statements, we believe one and not the other, but traditional modal logic cannot capture this. Justification logic, however, can, ascertaining that a reason to believe one statement only becomes a reason to believe the other in the presence of a reason for believing their equivalence. This has obvious application for artificial intelligence and philosophy, but authors Artemov (CUNY) and Fitting (emer., CUNY) explore this concept with a glamorous mathematical objective. Famed mathemetician Kurt Gödel could interpret intuitionist logic in a certain modal logic (S4), and could interpret a different modal logical (GL) in arithmetic, but failed to find an arithmetic interpretation of intuitionist logic. Justification logic now provides the bridge he sought between S4 and arithmetic. The authors pioneered the subject and between them own many of its major results; they also explain, and indeed sell it, very well. Summing Up: Recommended. All readership levels. --David V. Feldman, University of New Hampshire
Copyright American Library Association, used with permission.
Review by Choice Review
