Includes bibliographic references.
|Series||Annals of mathematics and artificial intelligence -- v. 1, no. 1/4|
|Contributions||Jeroslow, Robert G., 1942-.|
|LC Classifications||Q335 .A562 vol. 1, no. 1/4|
|The Physical Object|
|Pagination||372 p. ;|
|Number of Pages||372|
The class of Horn clause sets in propositional logic is extended to a larger class for which the satisfiability problem can still be solved by unit resolution in linear time. It is shown that to. A Horn clause is a clause with at most one positive literal, called the head of the clause, and any number of negative literals, forming the body of the clause. A Horn formula is a propositional formula formed by conjunction of Horn clauses. The problem of Horn satisfiability is solvable in linear time. Horn clauses. In this subsection we introduce a special class of formulae which are of particular interest for logic programming. Furthermore it turns out that these formulae admit an efficient test for satisfiability. Definition 9. A formula is a Horn formula if it is in CNF and every disjunction contains at most one positive literal. • Another useful class: Horn-SAT – A clause is a Horn clause if at most one literal is positive – If all clauses are Horn, then problem is Horn-SAT – E.g. Application: Checking that one finite-state system refines (implements) another 12 Phase Transitions in k-SAT • Consider a fixed-length clause model – k-SAT means that each clause containsFile Size: KB.
We propose an algorithm that prunes the search space for satisfiability in horn clauses and prove that the optimal solution is guaranteed to exist in the pruned space. The approach finds a model, if it exists, in polynomial time; otherwise it finds an interpretation that is most likely given the by: 1. Horn formulae are widely used in different settings that include logic programming, answer set programming, description logics, deductive databases, and . 4 CS Knowledge Representation M. Hauskrecht KB in Horn form • Horn form: a clause with at most one positive literal • Not all sentences in propositional logic can be converted into the Horn form • KB in Horn normal form: – Three types of propositional statements: • Rules • Facts • Integrity constraints (A∨¬B) ∧(¬A∨¬C ∨D) (B1 ∧B2 ∧KBk ⇒ A)File Size: KB. Introduction to Mathematics of Satisfiability. Introduction to Mathematics of Satisfiability book. By Victor W. Marek. Edition 1st Edition. First Published eBook Published 22 September Pub. location New York. Imprint Chapman and Hall an extension of Horn logic. View abstract. chapter 15 | 4 pages Conclusions. View Cited by:
0Reviews. This account of propositional logic concentrates on the algorithmic translation of important methods, especially of decision procedures for (subclasses of) propositional logic. Important classical results and a series of new results taken from the fields of normal forms, satisfiability and deduction methods are arranged in a uniform and complete theoretic framework. hand, the satisfiability of Horn clauses is decidable in polynomial time . For modal logics, it has been proved  that the satisfiability problems of the modal logics K, T, and S4 are log-space complete in PSPACE, while the satisfiability. Finite satisfiability. A problem related to satisfiability is that of finite satisfiability, which is the question of determining whether a formula admits a finite model that makes it true. For a logic that has the finite model property, the problems of satisfiability and finite satisfiability coincide, as a formula of that logic has a model if and only if it has a finite g: Horn logic. The Satisfiability Problem Cook’s Theorem: An NP-Complete Problem Restricted SAT: CSAT, 3SAT. 2 Boolean Expressions Boolean, or propositional-logic expressions are built from variables and constants using the operators AND, OR, and NOT. Constants are true and false, representedMissing: Horn logic.