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	Horn Logic - W3C RIF-WG Wiki
		Since the RIF charter mentions "Horn Logic" several times, this is an attempt to define the term more precisely.
		I propose to define "Horn Logic" as a formal language, which has a corresponding inference procedure, thus forming a formal system together.
		In relation to "Horn Logic" a "subset of standard Prolog" is a logic program with clauses ordered sequentialy, and atoms in the body ordered from left-to-right.
	www.w3.org /2005/rules/wg/wiki/Horn_Logic (502 words)

	[No title]
		Description logics (DLs) [Baader et al., 2003] are state-of- In [Schaerf, 1994], the complexity of concept subsump- the-art knowledge representation formalisms with applica- tion was contrasted with combined and data complexity of tions in many areas of computer science.
		A logic L A core property of (KB) is that it only contains clauses is between logics L1 and L2 if it contains at least the primi- of one of the forms given in Table 2; such clauses are called tives from L1 and at most the primitives from L2.
		The main limitation of Horn logic is its 0 0 inability to represent disjunctive information; however, its A 1 0 È main benefit is the existence of practical refutation proce- pl+ (C) pl- (C) ¬CC C È maxi sgn(pl+ (Ci)) dures.
	www.ijcai.org /papers/0326.txt (5086 words)

	Horn - Wikipedia, the free encyclopedia
		Horn (Chinese constellation), a constellation in Chinese astronomy
		Horn (Netherlands), a village in the municipality of Haelen
		Horn clause is a term in formal logic.
	en.wikipedia.org /wiki/Horn (438 words)

	Horn clause - Wikipedia, the free encyclopedia
		In logic, a Horn clause is a clause (a disjunction of literals) with at most one positive literal.
		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 of interest 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.
	en.wikipedia.org /wiki/Horn_clause (389 words)

	[No title] (Site not responding. Last check: )
		Ever since Bertrand Russell's time, the question whether logic is part of mathematics, or mathematics is part of logic, or neither, has been discussed, and I confess that I still do not know the answer.
		The emphasis in the former lecture [31] was on the connections between logic and computation.
		This is the proceedings of a conference held in Russia in 1992.
	www.mathcs.sjsu.edu /faculty/beeson/Papers/logcomp.html (1308 words)

	Chapter Ten: Formal Methods (Section 10.4)
		Horn clauses express a subset of statements of first-order logic.
		In other words, a horn clause has just one predicate in terms of a conjunction of predicates.
		Prolog limits predicate logic to horn clauses in order to ensure that there is a way to check that the given WFF is true.
	cs.allegheny.edu /wiki/cs290F2004/105 (355 words)

	King Horn: Introduction
		Horn begins as a frightened noble child who develops a love life, achieves several military victories, becomes a sophisticated strategist with his use of disguises and coded statements to Rymenhild, and ultimately wins back his love and his kingdom, both of which have been taken away from him unjustly.
		Rather than putting the heroine on a pedestal and praising her virtues, Horn is pursued by her; his physical beauty sparks a passion for him that drives Rymenhild wild (lines 256, 300, 956).
		For Lee C. Ramsay the poem "seems to say that internal dissension is the ultimate threat to a state." 9 Yet King Horn is not as much a "mirror for princes" as is Havelok the Dane; rather, it is more a chronicle of martial and romantic achievement, a chronicle concerned with political gains.
	www.lib.rochester.edu /camelot/teams/hornint.htm (1859 words)

	Rewriting Logic as a Logical and Semantic Framework (Site not responding. Last check: )
		Rewriting logic s proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems.
		The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of ``sequent,'' is discussed in detail.
		Finally, the use of rewriting logic as a logic of change that overcomes the frame problem in AI is also discussed.
	maude.cs.uiuc.edu /papers/abstract/MMlogframework_1993.html (314 words)

	[No title]
		The horn structure is a logical structure made up entirely of implications (p => q).
		It verifies existance by backward chaining and substitution The (Aima) Horn Clause I chose the Horn Clause, which is a logical method, to investigate.
		I eventually hit on loading the Aima file and the logic files (which I used last semester in 223) in addition to the Horn file.
	www.ecst.csuchico.edu /~bills/webpage/HornAnalysis (700 words)

	Monadic Constructs for Logic Programming (Site not responding. Last check: )
		Interestingly enough, the idea of the intrinsic usefulness of higher-order constructs seems to be back again in the functional programming community after the proof of expressiveness of some essentially high-order monad constructs (used for instance in describing state transformers and constant time array operations) in the papers of Philip Wadler.
		However, its correctness in the absence of occur check and the need for extra logical tests to detect `the end' of such lists make it less interesting especially when a concept of lazy function-list is available as it is the case with \lambdaProlog-Mali.
		However, ideas alike in substance are present in Peter VanRoy's Extended DCGs [edcg] and their Wild-Life [kaci91:PLILP] counterparts, which encapsulate, through a preprocessing technique, a concept of state similar to the state transformers in functional programming [wadler:comprehending:lfp:90] and some of the morphisms we have described are `implicitely' known to good Prolog programmers.
	logic.csci.unt.edu /tarau/research/PapersHTML/monadic.html (3421 words)

	joint-committee Mailing List Archive: RuleML's Horn logic program semantics: draft (inline'd and attached)
		Likewise, we define the classical version of a Horn LP rulebase R to consist of the classical versions of every rule in R. In Horn LP, each rule of form (1) can be viewed as universally quantified at outermost scope, with the notation simply leaving this quantification implicit.
		The model of a Horn logic program R is the smallest subset S of HB such that for any rule of form (1) in R, if B_1,..., B_m are each in S, then H is also in S. Notationally, this model is denoted by mod(R).
		Relationship to Horn FOL: The model of R is the least Herbrand model, in the sense that it is the greatest lower bound w.r.t.
	www.daml.org /listarchive/joint-committee/1346.html (2090 words)

	Re: A FIXPOINT THEOREM IN LINEAR LOGIC
		The other, found by Schroeder in 1895 [Sch95], is to strip out the notion of number and generalize the notion of chain to the notion of reflexive transitive closure of any binary relation (Dedekind defined "chain" only for functions).
		QED This equational axiomatization of transitive closure is based on Segerberg induction for propositional dynamic logic, 1977.
		As it stands it can be read as saying that if after some number of a's b holds, then either b holds now or after some number of a's b is still false but will hold after one more a.
	www.seas.upenn.edu /~sweirich/types/archive/1992/msg00035.html (994 words)

	RIF-WG: W3C Rule Interchange Format Working Group Charter
		Not every rule engine is or should be able to process full Horn Logic rules; they are Turing complete, hence undecidable (the deductive closure of a Horn rule set is infinite in the general case).
		These syntactic extensions to Horn logic (in some cases extended with negation), provide convenient syntax with no additional expressive power.
		The ISO Common Logic effort aims to produce "a language designed for use in the interchange of knowledge among disparate computer systems.
	www.w3.org /2005/rules/wg/charter (4761 words)

	Description Logic Programs: Combining Logic Programs with Description Logic
		Declarative logic programs (LP) is the KR whose semantics underlies in a large part the four families of rule systems that are currently most commercially important--SQL relational databases, OPS5-heritage production rules, Prolog, and Event-Condition-Action rules--as well as the proposals for rules in context of the Semantic Web.
		Definite Horn FOL requires that all variables are universally quantified (at the outer level of the rule), and restricts logical connectives in certain ways.
		One obvious consequence of the restriction on quantifiers is that it is impossible to assert the existence of individuals whose identity might not be known.
	www2003.org /cdrom/papers/refereed/p117/p117-grosof.html (6713 words)

	Information and Computation Bibliography (Site not responding. Last check: )
		An extension of Horn Clause Logic is defined based on the introduction of a synchronization operator.
		Generalized Horn Clauses (GHC) are introduced though an informal descriptionof their operational semantics, which allows discussion of some typical synchronization problems.
		Finally, the relation between GHC and Horn Clauses is analyzed, and it is proved that Horn Clause Logic is strictly included in the Generalized Horn Clause Logic.
	theory.lcs.mit.edu /~iandc/References/falaschilp1984:36.html (172 words)

	Logic Programming
		In this latter form it is a variant of the first-order predicate calculus known as Horn clause logic.
		There are two solutions, the first is to change the logic and permit infinite terms, the second is to introduce the occur check with the resulting loss of efficiency.
		The query is a logical consequence of the first two clauses but Prolog cannot determine that fact and enters an infinite derivation tree.
	burks.brighton.ac.uk /burks/pcinfo/progdocs/plbook/logic.htm (5266 words)

	The World Wide Web Virtual Library: Logic Programming
		Logic Programming Group and searchable papers related to logic programming by people at Department of Computing, Imperial College, London, UK.
		Mercury, a pure logic programming language designed for the development of efficient and robust real-world applications, based on strong types and modes.
		RELFUN extends Horn logic by higher-order syntax, first-class finite domains, and eager expressions of non-deterministic, non-ground functions, explicitly distinguished from structures.
	vl.fmnet.info /logic-prog (1454 words)

	Horn Clause Logic
		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.
		Distribution of this work or any derivative works in whole or in part in standard (paper) book form for commercial purposes is prohibited unless prior permission is obtained from the copyright holder.
	cs.wwc.edu /~aabyan/Logic/Horn.html (222 words)

	[2-7] Free Logic Programming Systems
		The foundation of ALF is Horn clause logic with equality which consists of predicates and Horn clauses for logic programming, and functions and equations for functional programming.
		Like Prolog and other existing logic programming languages, it is a very high-level language that allows programmers to concentrate on the problem rather than the low-level details such as memory management.
		Mercury's type system is based on many-sorted logic with parametric polymorphism, very similar to the type systems of modern functional languages such as ML and Haskell.
	www.faqs.org /faqs/prolog/resource-guide/part2/section-8.html (590 words)

	Open Directory - Computers:Programming:Languages:Logic-based
		This category is on programming languages and documents that fully or partially support the basic principles of logic programming: declarative, relational programming based on first-order logic, via Horn clauses, where authors write databases of facts and rules (clauses), and users supply goals, which programs work to prove via resolution or backward chaining.
		Functional logic languages are a class of multiparadigm language, where the goal is to combine the two most important types of declarative languages: functional languages and logic-based languages.
		Compared to pure logic languages, functional logic languages are more efficient operationally since functions allow more efficient evaluation strategies (lazy evaluation, deterministic reductions) than predicates.
	dmoz.org /Computers/Programming/Languages/Logic-based/desc.html (316 words)

	Inference in First Order Logic: Horn Clauses
		This fails because a the variable may never occur in the term it is being unified with.
		Generalized modus ponens requires sentences to be in a standard form, called Horn clauses after the mathematician Alfred Horn.
		A Horn clause is a sentence of the form
	www.sdsc.edu /~tbailey/teaching/cse151/lectures/chap09a.html (1010 words)

	Cut and Weakening in Fuzzy Horn Logic -- Vychodil 13 (5): 599 -- Logic Journal of IGPL
		Cut and Weakening in Fuzzy Horn Logic -- Vychodil 13 (5): 599 -- Logic Journal of IGPL
		the context of equational fragment of Pavelka-style fuzzy logic
		Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues.
	jigpal.oxfordjournals.org /cgi/content/short/13/5/599?rss=1 (184 words)

	The Limits of Horn Logic Programs
		It is proved that this property is not true in general but holds if Horn logic programs satisfy an assumption which can be syntactically checked and be satisfied by a class of Horn logic programs.
		We also prove that if a finite Horn logic program satisfies this assumption, then the least Herbrand model of this program is recursive.
		Finally, by use of the concept of stability from dynamical systems, we prove that this assumption is exactly a sufficient condition to guarantee the stability of fixed points for Horn logic programs.
	www.nlsde.buaa.edu.cn /~kexu/papers/iclp02-abstract.htm (193 words)

	Information and Control -- 1984 (Site not responding. Last check: )
		A synchronization logic: Axiomatics and formal semantics of generalized Horn clauses.
		Erratum: The satisfiability problem for a class consisting of Horn sentences and non-Horn sentences in proportional logic.
		Arbitrary versus periodic storage schemes and tessellations of the plane using one type of polyomino.
	theory.lcs.mit.edu /~iandc/ic84.html (243 words)

	CS 6905 Functional and Logic Programming
		Functional programming starts with nested function applications, as found in most programming languages, and leads to powerful higher-order and concurrent languages: it developed from Lisp and Scheme to Standard ML, Haskell, Erlang, and Pizza (a version of Java).
		Logic programming starts with Horn-logic facts and rules and leads to logic markup languages for business rules: it developed from Prolog to BRML, RuleML, and Common Logic.
		This course will treat the core of functional and logic programming in an integrated manner as an example of declarative programming.
	www.cs.unb.ca /~boley/FLP-2004/index.html (288 words)

	Logic (Subsystem of AIMA Code)
		We need a new language for logical expressions, since we don't have all the nice characters (like upside-down A) that we would like to use.
		Try to convert sentence to a Horn clause, or a conjunction of Horn clauses.
		A Horn clause (in INF) is an implication with atoms on the left and one atom on the right.
	www.cs.berkeley.edu /~russell/code/doc/overview-LOGIC.html (1309 words)

	Horn Logic Denotations
		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.
		G. Gupta "Horn Logic Denotations and Their Applications," The Logic Programming Paradigm: A 25 year perspective, Springer Verlag.
	www.cs.nmsu.edu /~gupta/sem.html (358 words)

	FOL RuleML: The First-Order Logic Web Language
		This paper describes First-Order Logic RuleML (FOL RuleML), which is planned to be the FOL sublanguage of RuleML 0.9, the rule component of SWRL FOL, and an FOL content language for SWSI.
		The markup language for first-order logic introduced here is itself proposed as a central RuleML sublanguage, extending the design of RuleML 0.87.
		In the spirit of the logic in 'FOL RuleML', the conjoined clauses of a rulebase are connected by an explicit 'And'.
	www.ruleml.org /fol (4133 words)

	List of Publications of Catuscia Palamidessi (Site not responding. Last check: )
		Control flow versus logic: a denotational and a declarative model for Guarded Horn Clauses.
		An approach to the declarative semantics of synchronization in logic languages.
		On the declarative semantics of Horn Clause Logic-based languages.
	www.cse.psu.edu /~catuscia/publications.html (1678 words)

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