Some Results in Dynamic Model Theory

Abstract

Traditional model theory (Chang and Keisler 1973, Bell and Slomson 1971), like classical predicate logic, is static in nature. Models, valuations of variables, and truth values of predicates are regarded as fixed and immutable. This tradition has surely contributed to the dominance of denotational over operational semantics in programming languages. It is somewhat ironic that first-order predicate logic is in general inadequate for handling even the most elementary and pervasive of logical constructions in computer science, namely induction. For this reason, and for its general lack of programmability, one might argue that the emphasis on first-order predicate logic in the undergraduate computer science curriculum may be detrimental to the development of sound algorithmic reasoning.