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Natural Language Processing Associated with Expert Systems
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
It should be noticed that, under the influence of the programming language PROLOG, several modern FOPC-based representation systems are, in reality, “Horn clauses systems.” These systems are characterized by two important properties. The first is that, in these systems, all logical formulas are converted to a normal form, called “clause form.” Horn clauses are disjunctive logic formulas with at most one positive (unnegated) “literal”; a literal is an atomic formula P (term1, …. termn) for some predicate P, where “term…” are, as usual, the arguments. Restriction to Horn clauses is conceptually equivalent to disallowing implications of the type “A → B ν C,” i.e., giving rise to disjunctions within the body of the clause. The second property consists of the fact that Horn clauses systems make use of a single deductive mechanism based on Robinson’s “resolution principle.” The resolution principle tries to prove that a “theorem,” i.e., a clause whose truth value is as yet unknown, can be derived from a set of “axioms,” i.e., clauses that are assumed to be true. This principle is based on the notion of contradiction, i.e., a clause and its negation cannot both be true.
Automatic Test Pattern Generation
Published in Louis Scheffer, Luciano Lavagno, Grant Martin, EDA for IC System Design, Verification, and Testing, 2018
Kwang-Ting (Tim) Cheng, Li-C. Wang
Given a finite set of variables, V, over the set of Boolean values B∈{0,1}, a literal, l or l¯ is an instance of a variable v or its complement ¬v, where v∈Vclause ci, is a disjunction of literals (l1∨l2∨…∨ln). A formula f, is a conjunction of clauses c1∧c2∧…∧cm. Hence, a clause is considered as a set of literals, and a formula as a set of clauses. An assignment A satisfies a formula f if f (A) = 1. In a SAT problem, a formula f is given and the problem is to find an assignment A to satisfy f or prove that no such assignment exists.
Automatic Test Pattern Generation
Published in Luciano Lavagno, Igor L. Markov, Grant Martin, Louis K. Scheffer, Electronic Design Automation for IC System Design, Verification, and Testing, 2017
Kwang-Ting (Tim) Cheng, Li-C. Wang, Huawei Li, James Chien-Mo Li
Given a finite set of variables, V, over the set of Boolean values B ∈ {0, 1}, a literal, l or Ī is an instance of a variable v or its complement ¬v, where v ∈ V. A clause ci, is a disjunction of literals (l1 ∨ l2 ∨ ⋯ ∨ ln). A formula f, is a conjunction of clauses c1 ∧ c2 ∧ ⋯ ∧ cn. Hence, a clause is considered as a set of literals, and a formula as a set of clauses. An assignment A satisfies a formula f if f (A) = 1. In a SAT problem, a formula f is given and the problem is to find an assignment A to satisfy f or prove that no such assignment exists.
A Causal Map Analysis of Supply Chain Decentralization
Published in Journal of Computer Information Systems, 2022
In order to describe how theory formalization works, let us start by recalling the basic principles of propositional logic.36,37 We first define its basic components, the predicates, or clauses, which are the statements we make about the relationships between variables. The formulas of propositional logic are obtained recursively from the basic axioms through the use of connective symbols, which (in this article) are not (), and (), causal implication (). We discuss this in detail in the next subsection. In propositional logic, each clause is assigned a truth-value (true or false). A clause is said to be consistent if it can be interpreted as true and inconsistent otherwise. A clause is said to be valid (also known as a tautology) if it is always interpreted as true.
A MaxSAT based approach for QoS cloud services
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
Abderrahim Ait Wakrime, Said Jabbour, Nabil Hameurlain
We first introduce the satisfiability problem (SAT) and some necessary notations. SAT corresponds to the problem of deciding if a formula of propositional classical logic is consistent or not. It is one of the most studied NP-complete decision problem. We consider the conjunctive normal form (CNF) representation for the propositional formulas. A CNF formula Φ is a conjunction of clauses, where a clause is a disjunction of literals. A literal is a positive (p) or negated () propositional variable. The two literals p and are called complementary. We denote by the complementary literal of l, i.e. if l=p, then and if , then . For a set of literals L, is defined as . A CNF formula can also be seen as a set of clauses, and a clause as a set of literals. Let us recall that any propositional formula can be translated to CNF using linear Tseitin's encoding [5]. We denote by (respectively ) the set of propositional variables (respectively literals) occurring in Φ.
An extensible circuit-based SAT solver
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2020
A propositional theory in Conjunctive Normal Form (CNF) over a set of variables is a conjunction of disjunctions of literals, where a literal is either an instance of a variable or its negation. The task in Satisfiability (SAT) is to determine whether a complete assignment to the variables of the theory exists such that all clauses (disjunctions) are satisfied (at least one of the literals of each clause is ). When a literal in a clause is set to it is removed from the clause reducing the clause size. A clause becomes unit under a partial assignment to variables if the clause is left with only one literal, which must be set to as a necessary condition for satisfiability, a phenomenon known as unit propagation. The clause which forces a literal assignment after becoming unit is called antecedent clause of the assigned literal.