Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Denotational semantics: a methodology for language development
Denotational semantics: a methodology for language development
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Eliminating the fixed predicates from a circumscription
Artificial Intelligence
Computability, complexity, and languages (2nd ed.): fundamentals of theoretical computer science
Computability, complexity, and languages (2nd ed.): fundamentals of theoretical computer science
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Guarded fixed point logics and the monadic theory of countable trees
Theoretical Computer Science - Complexity and logic
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Elements of Finite Model Theory
Elements of Finite Model Theory
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The concept of minimization is widely used in several areas of Computer Science. Although this notion is not properly formalized in first-order logic, it is so with the logic MIN(FO) [13] where a minimal predicate P is defined as satisfying a given first-order description φ(P). We propose the MIN logic as a generalization of MIN(FO) since the extent of a minimal predicate P is not necessarily unique in MIN as it is in MIN(FO). We will explore two different possibilities of extending MIN(FO) by creating a new predicate defined as the union, the U-MIN logic, or intersection, the I-MIN logic, of the extent of all minimal P that satisfies φ(P). We will show that U-MIN and I-MIN are interdefinable. Thereafter, U-MIN will be just MIN. Finally, we will prove that simultaneous minimizations does not increase the expressiveness of MIN, and that MIN and second-order logic are equivalent in expressive power.