Quantifier Elimination-Based Constraint Logic Programming
نویسنده
چکیده
We present an extension of constraint logic programming, where the admissible constraints are arbitrary first-order formulas over some domain. Constraint solving is realized by effective quantifier elimination. The current realization in our CLP(RL) system provides as possible domains R, C, and Qp for primes p. In R and C we admit arbitrary degrees in our constraints. In Qp we restrict to linear formulas. The arithmetic is always exact. We describe the conceptual advantages of our approach and the capabilities of CLP(RL). [email protected], http://www.fmi.uni-passau.de/ ̃sturm/
منابع مشابه
Generalized Constraint Solving by Elimination Methods
In this survey paper on our work in the field of constraint solving techniques, we discuss generalizations of constraint solving over various domains. These generalizations comprise paradigms from both computational algebra (e.g. parameterization) as well as from logic (e.g. expressiveness of full first-order logic). The domains include real numbers, p-adic numbers, integers, differential field...
متن کاملTree Grammars for the Elimination of Non-prenex Cuts
Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs with prenex Π1-cuts in classical first-order logic corresponds to computing the language of a particular type of tree grammars. The present paper extends this connection to arbitrary (i.e. non-prenex) cuts without quantifier alternations. The ke...
متن کاملEarly Steps of Second-Order Quantifier Elimination beyond the Monadic Case: The Correspondence between Heinrich Behmann and Wilhelm Ackermann 1928-1934 (Abstract)
This presentation focuses on the span between two early seminal papers on second-order quantifier elimination on the basis of first-order logic: Heinrich Behmann’s Habilitation thesis Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem (Contributions to the algebra of logic, in particular to the decision problem), published in 1922 as [4], and Wilhelm Ackermann’s Untersuchunge...
متن کاملFaster Quantifier Elimination from Similar Pre-solved Problems for Visual Problem Solving
We have been building a general purpose diagrammatic reasoning (DR) architecture that is being deployed to solve a variety of problems in different domains, such as entity re-identification, ambush analysis, planning in urban scenario in the military domain, problems in mechanics and civil engineering, theorem proving in Euclidean geometry, and set theory problems using Venn diagrams. A vital c...
متن کاملOpen-World Logic Programs: A New Foundation for Formal Specifications
Recent advances in decision procedures and constraint solvers can enable a new generation of formal specification languages. In this paper we present a new semantic foundation for formal specifications, called open-world logic programming, which integrates with state-of-theart solvers. Analysis, verification, and synthesis problems on open-world logic programs can be converted to constraints by...
متن کامل