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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.
H
Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017
Horn clause also known as a definite clause, it is a clause with one positive literal. It is written as a disjunction A ∨ ⌜ B1 ∨…∨ ⌜Bn or ⌜B1 ∨…∨ ⌜Bn with k < 1 positive atomic formulas. Horn clauses correspond to definite rules (for k = 1 ) or goals (for k = 0), respectively. Horn clauses can express a subset of statements of first order logic. See clausal form.
Introduction to Expert Systems
Published in Chris Nikolopoulos, Expert Systems, 1997
An undesirable effect of the CWA is that it can render knowledge bases inconsistent. Consider the knowledge base D consisting of just the fact A∨B. Since A cannot be derived from the knowledge base, then A does not belong to the completion of D. Similarly, B does not belong to the completion of D. If the CWA is in effect, we can conclude that ¬A and ¬B are true and can be augmented to the knowledge base. But now the knowledge base is inconsistent. As it actually turns out, whenever a clause has two or more positive atomic formulas and at least two of them cannot be deduced from the knowledge base, then the CWA hypothesis renders the knowledge base inconsistent. If we limit ourselves to knowledge bases with clauses of at most one positive literal, then the CWA does not introduce the inconsistency problem. A clause of at most one positive literal is called a Horn clause. The logic programming language Prolog employs the CWA and only Horn clauses, as consistency is of paramount importance. A horn clause with one positive literal can be rewritten in the form of a rule with only one literal at its head. For example, the Horn clause ¬p(X)∨q(X,Y)∨s(X) is equivalent to the rule p(X)∧q(X)⇒s(X). It should be noted however that the Horn clause based logic is more restrictive than first order predicate logic. To be able to assure consistency, we sacrifice the full expressive power of first order predicate logic. For example, it is not possible to express the following set of clauses in Horn clause format or Prolog syntax:
Survey on frontiers of language and robotics
Published in Advanced Robotics, 2019
T. Taniguchi, D. Mochihashi, T. Nagai, S. Uchida, N. Inoue, I. Kobayashi, T. Nakamura, Y. Hagiwara, N. Iwahashi, T. Inamura
LP is essentially a declarative programming paradigm based on formal logic. LP has its roots in automated theorem proving, where the purpose is to test whether or not a logic program Γ can prove a logical formula, or query, ψ, i.e. or . For computational efficiency, the language used in logic programs is typically restricted to a subset of first-order logic (e.g. Horn clauses [32]). From a reasoning perspective, LP serves as an inference engine. Hobbs et al. [33] propose an Interpretation as Abduction framework, where natural language understanding is formulated as abductive theorem proving. In this context, a logic program Γ is a commonsense knowledge base (e.g. ) and a query ψ will be a question that is of interest (e.g. ).