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	Horn clause - Wikipedia, the free encyclopedia
		The relevance of Horn clauses to theorem proving by first-order resolution is that the resolution of two Horn clauses is a Horn clause.
		Horn clauses are also critical in computational complexity, where the problem of finding a set of variable assignments to make a conjunction of Horn clauses true is a P-complete problem, sometimes called HORNSAT.
		The name "Horn clause" comes from the logician Alfred Horn, who first pointed out the significance of such clauses in 1951, in the article "On sentences which are true of direct unions of algebras", Journal of Symbolic Logic, 16, 14-21.
	en.wikipedia.org /wiki/Horn_clause (329 words)

	Horn (disambiguation) - Wikipedia, the free encyclopedia
		Horn (Chinese constellation), a constellation in Chinese astronomy
		Horn (diacritic), a diacritic mark used to indicate that a normally rounded vowel such as o or u is to be pronounced unrounded
		Horn clause, a particular kind of clause in formal logic
	en.wikipedia.org /wiki/Horn (225 words)

	Horn clause -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		This form shows that Horn clauses are a subset of those in (Click link for more info and facts about conjunctive normal form) conjunctive normal form, in which at most one of the terms is a positive literal, and the rest are negated.
		Horn clauses play a basic role in (Creating a program that enables the computer to reason logically) logic programming and are important for (Click link for more info and facts about constructive logic) constructive logic.
		Horn clauses are also critical in (Click link for more info and facts about computational complexity) computational complexity, where the problem of finding a set of variable assignments to make a conjunction of Horn clauses true is a (Click link for more info and facts about P-complete) P-complete problem, sometimes called HORNSAT.
	www.absoluteastronomy.com /encyclopedia/h/ho/horn_clause.htm (428 words)

	SUNY Geneseo CSci 341 Logic Programming Part 2 Spring 2000
		This is the heart of resolution as a theorem-proving technique: If a series of resolutions simplifies a system of Horn clauses to nothing, it means that the system is inconsistent (i.e., to satisfy it, at least one term in an empty clause must be true).
		So to "prove" a statement, phrase it's negation as a Horn clause, add it to a Horn clause system of "axioms", and run resolution until either it can no longer simplify the system (the theorem isn't provable), or it produces an empty clause (the theorem is true).
		Typically the theorem to be proven is a single proposition, e.g., A, its negation is thus (not A), i.e., a headless Horn clause.
	www.cs.geneseo.edu /~baldwin/csci341/spring2000/lp0424.html (418 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		(1) (20 points) A Horn clause is a disjunction of literals with at most one positive literal in it.
		Your first work is to implement "translate1" to translate a Horn clause from the first representation to the new representation.
		After reading from this file, the setting of this global variable will be: ((A or not B) (B) (not A or not B or not C or not A) (C)) Translate all Horn clauses to the new representation and remove all redundant literals in them, assigning the result to the new global variable new-inputs.
	www.umiacs.umd.edu /~bonnie/courses/cmsc421-01/lab1.txt (792 words)

	Tools for program development
		Having Horn clause definitions of types is useful in itself for runtime type checks, test data generation et cetera.
		These Horn clause definitions may also be refined by adding further constraints, for example, refining the definition of a binary tree to obtain the definition of a binary search tree.
		One challenge is taking a known transformation from regular types to higher order functions and generalising it to Horn clause definitions which may not correspond to regular types.
	www.cs.mu.oz.au /~lee/papers/hose2/naish/node13.html (618 words)

	Horn Analysis [ReadMe] (Site not responding. Last check: 2007-10-18)
		The horn structure is a logical structure made up entirely of implications (p => q).
		The (Aima) Horn Clause I chose the Horn Clause, which is a logical method, to investigate.
		**postcondition: An instance of a knowledge structure which is capable of indexing Horn statements (in a hash table data structure) by the predicate on the right-hand side of the clause**.
	www.ecst.csuchico.edu /~bills/webpage/HornReadme.html (448 words)

	Fluents: a Uniform Extension of Kernel Prolog for Reflection and Interoperation with External Objects
		While the semantics of a fluent-enabled, multi-interpreter programs cannot be expressed in a trivial way in terms of one-interpreter Horn Clause LD-resolution, their operational semantics reuses common programming knowledge as basic as reading a sequence from a file or using an iterator.
		Unlike pure Horn Clause Prolog and unlike weaker languages based on Prolog + negation, which have been extensively studied in the past, Kernel Prolog has enough power to be used as a basis for building compact Prolog implementations as well as for modular library components.
		Clause and (wide, Unicode compatible) character Readers are seen as instances of Sources and therefore benefit form Source composition operations.
	www.binnetcorp.com /kprolog/fluents.html (5366 words)

	AROUND THE HORN: Contract clause may hurt Frank
		CHICAGO -- The White Sox invoked a contract clause that drastically reduces Frank Thomas' salary, clearing the way for the two-time MVP to become a free agent.
		The club sent the designated hitter/first baseman a letter Oct. 6, telling him it was invoking a "diminished skills" clause, reducing his base pay to $250,000 and deferring most of his nearly $10-million salary.
		Thomas' contract says he had seven days following the notification to choose whether to become a free agent, although the sides have discussed extending that deadline.
	www.freep.com /sports/baseball/horn16_20021016.htm (280 words)

	CSE 663, Fall 2003, Advanced Topics in Knowledge Representation (Site not responding. Last check: 2007-10-18)
		After McKinsey's paper in 1943, Alfred Tarski suggested investigating a more general class of sentences which are like Horn clauses except that they have arbitrarily many existential and universal quantifiers at the beginning.
		The sentences which Tarski described are now known as Horn sentences, because Tarski's colleague Alfred Horn (1951) responded to Tarski's suggestion by showing that one of McKinsey's theorems...
		Horn, Alfred (1951), "On Sentences which Are True of Direct Unions of Algebras", Journal of Symbolic Logic 16: 14-21.
	www.cs.buffalo.edu /~rapaport/663/F03/horn.html (290 words)

	CogSci 108b: Unification and Horn-Clause Theorem-Proving
		A "clause" in our representation of predicate logic will be a list of literals.
		It will be interpreted as a disjunction, with any variables in the literals interpreted as being universally quantified (i.e., as if there were a "forall" statement in front).
		Note that the literal in clause C1 and the expression E1 are very similar.
	cogsci.ucsd.edu /~batali/108b/lectures/cunify.html (2896 words)

	[No title]
		Creates the file and ; writes on it a set of clauses with the same meaning as S but in the ; syntax of the Illinois prover.
		Clauses ; are assumed to be multisets, with their literals kept in order.
		; When a clause C is removed because it is an instance of a clause D, D's ; parents are modified to include C's parents.
	www.cs.unc.edu /~plaisted/lp/tptools.ss (3101 words)

	Horn clause - FOLDOC Definition (Site not responding. Last check: 2007-10-18)
		A set of atomic literals with at most one positive literal.
		Horn clauses can express a subset of statements of first order logic.
		A definite clause is a Horn clause that has exactly one positive literal.
	www.nightflight.com /foldoc-bin/foldoc.cgi?Horn+clause (114 words)

	Citations: Horn Clause Queries and Generalizations - Chandra, Harel (ResearchIndex) (Site not responding. Last check: 2007-10-18)
		Chandra, A., and Harel, D., Horn Clauses Queries and Generalizations.
		this result also for Datalog, the language of function free logic programs (known also as Horn clause programs) which plays a major role in database theory [1] Datalog is essentially the existential fragment of fixpoint logic, i.e.
		On the Impact of Stratification on the Complexity of..
	citeseer.ist.psu.edu /context/45254/0 (2773 words)

	Horn clause - OneLook Dictionary Search
		Horn clause : Free On-line Dictionary of Computing [home, info]
		Horn Clause : Eric Weisstein's World of Mathematics [home, info]
		Horn clause : FOLDOP - Free On Line Dictionary Of Philosophy [home, info]
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=Horn+clause (104 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		It verifies existance by backward chaining and substitution The (Aima) Horn Clause I chose the Horn Clause, which is a logical method, to investigate.
		Using this system is was possible to run the system as follows: Start the run by loading aima.fasl and aima-loading 'logic.
		(=> P (Q x))), then sentence is added to the hash table for Q. (defmethod retract ((kb horn-kb) sentence) (for each clause in (conjuncts (->horn sentence)) do (deletef clause (gethash (op (arg2 clause)) (horn-kb-table kb)) :test #'renaming?))) ##precondition: The hash table horn-kb made up of horn clauses.
	www.ecst.csuchico.edu /~bills/webpage/HornAnalysis (700 words)

	Questions9b
		YES, because if you can represent your axioms as Horn clauses, then FC will eventually find a proof.
		Given the top two clauses of figure 9.5, what is the resolvent (output of the resolution rule)?
		There are 3 tricks to resolution theorem proving: The normal form, the resolution rule and one other trick.
	www.pitt.edu /~vanlehn/FoundationsOfAI00/Questions9b.htm (451 words)

	[No title]
		(conjuncts q))) (warn "~A, converted to ~A, is not a Horn clause." p q)) q)) ;;;; Auxiliary Functions (defun cnf1->inf1 (p) ;; P is of the form (or (not a) (not b)...
		;;; Each clause is represented by separate lists of symbols ;;; that appear positively and negatively; the lists are stored ;;; in arrays (cpos and cneg) indexed by clause number.
		;;; The arrays vpos and vneg are indexed by symbol number and ;;; list the clauses in which the symbol appears positviely and negatively.
	www.cs.berkeley.edu /~russell/classes/cs289/f04/assignments/sat289.lisp (1167 words)

	Horn Clause Logic (Site not responding. Last check: 2007-10-18)
		Horn clauses are used in the programming language Prolog.
		If n always is 1 then the logic is called Horn Clause Logic which is equivalent in computational power to the Universal Turing Machine.
		This material may be distributed only subject to the terms and conditions set forth in the Open Publication License, v0.4 or later (the latest version is presently available at
	cs.wwc.edu /~aabyan/Logic/Horn.html (222 words)

	Horn Logic Denotations (Site not responding. Last check: 2007-10-18)
		Coupled with partial evaluation this has numerous applications from building provably correct efficient compilers (sequential or parallelizing), to automatic generation of efficient implementations and abstract interpreters, to checking program correctness, etc. This project is being done in collaboration with University of Copenhagen (Denmark) and Southampton (UK).
		Use of Horn Clause Logic to specify denotational semantics is based on the observation that a notation based on Horn Clauses (pure Prolog) and Constraints facilitates inference of program properties, program transformations, etc., much more easily than the Lambda Calculus.
		There are a number of papers written on applications of Horn Clause Denotations to various fields.
	www.cs.nmsu.edu /~gupta/sem.html (358 words)

	TANKA/MaLTe Terminology
		An ILP technique that reverses the single step resolution rule and induces the left-side clause (e.g., given C_2 and D, induce C_1 such that D is the resolvent of C_1 and C_2.
		Yet another term for the module that constructs Horn Clauses from semantic structures.
		If the connected constituents are clauses, then the semantic relationship is a CLR; if the constituents are a verb and an argument of the verb, the semantic relationship is a Case; if the constituents are a noun and a noun-modifier, the relationship is an
	www.csi.uottawa.ca /~kbarker/terminology.html (584 words)

	A Petri-Net-Based Algorithm for Proofs in Horn Clause Propositional Logic. (Site not responding. Last check: 2007-10-18)
		Abstract: A Petri-net-based algorithm for the satisfiability problem in the Horn clause propositional logic is presented.
		The problem is defined by: given a set H of Horn clauses and a query Q, determine whether or not Q is satisfiable over H. An O(v²c) algorithm for finding a proof procedure of the problem, where v and c are the numbers of variables and clauses, respectively, is proposed.
		The time complexity of the following problem is analyzed: finding a smallest modification to obtain a query Q' and a set H' of Horn clauses over which Q' is satisfiable if Q is not satisfiable over H. Approximation algorithms are presented.
	www.informatik.uni-hamburg.de /TGI/pnbib/w/watanabe_t5.html (185 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		;;; -- Mode: Lisp; Syntax: Common-Lisp; -- File: logic/horn.lisp ;;;; Logical Reasoning in Horn Clause Knowledge Bases (defstructure horn-kb ;; Index all Horn sentences by the predicate on the right-hand side.
		See [p 275], but notice that this implementation is different.
		(for each clause in (gethash (op goal) (horn-kb-table kb)) do (let ((new-clause (rename-variables clause))) (back-chain-each kb (append (conjuncts (arg1 new-clause)) (rest goals)) (unify goal (arg2 new-clause) bindings) fn)))))))))
	aima.cs.berkeley.edu /lisp/logic/algorithms/horn.lisp (102 words)

	Logic (Subsystem of AIMA Code)
		A literal is an atomic clause or a negated atomic clause.
		A Horn clause (in INF) is an implication with atoms on the left and one atom on the right.
		internally, clauses are in minimal-cnf format, which is cnf without the and/or.
	www.cs.berkeley.edu /~russell/code/doc/overview-LOGIC.html (1309 words)

	[No title]
		(conjuncts q))) (warn "~A, converted to ~A, is not a Horn clause." p q)) q)) (defun logic (sentence) "Canonicalize a sentence into proper logical form." (cond ((stringp sentence) (->prefix sentence)) (t sentence))) ;;;; Auxiliary Functions (defun cnf1->inf1 (p) ;; P is of the form (or (not a) (not b)...
		(sentence) "A literal is an atomic clause or a negated atomic clause." (or (atomic-clause?
		(sentence) "A Horn clause (in INF) is an implication with atoms on the left and one atom on the right." (and (eq (op sentence) '=>) (every #'atomic-clause?
	aima.cs.berkeley.edu /lisp/logic/algorithms/normal.lisp (412 words)

	DNA Implementation of Simple Horn Clause Computation - Kobayashi, Yokomori, Sampei, Mizobuchi (ResearchIndex) (Site not responding. Last check: 2007-10-18)
		This method enables us to compute logical consequences of a given set of simple Horn clauses in parallel and takes advantage of potentially huge number of molecular CPUs of DNA computers.
		Further, we show that the method is nicely applied to the parallel implementation of a grammatical recognition algorithm which is based on `dynamic programming.
		On the other side, the theoretical research on DNA computing comprises attempts to model the process in general, and to give it a...
	citeseer.ist.psu.edu /kobayashi97dna.html (601 words)

	Cetus Links: 18,452 Links on Objects and Components / Prolog
		A horn clause consists of a sought implication (a goal clause), and a set of clauses that must be be proven separated by
		To represent just a fact instead of a rule, you specify just the head part of the horn clause (An implication with no conditions required to make it true is essentially a fact).
		But if a variable can not be bound for a given clause, that clause fails.
	www.cetus-links.org /oo_prolog.html (2177 words)

	One binary Horn clause is enough (Site not responding. Last check: 2007-10-18)
		The proof is based on a remarkable and not enough known codification of any computable function by unpredictable iterations proposed by.
		Then, we prove effectively by logical transformations that all conjunctive formulas of Horn clauses can be translated into an equivalent conjuctive 4-formula (as above).
		Some consequences are presented in several contexts (mathematical logic, unification modulo a set of axioms, compilation techniques and other program patterns).
	www.ps.uni-sb.de /Papers/paper_info.php?label=stacs94 (162 words)

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