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Topic: Negation as failure

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	CILOG User Manual -- 10 Negation-as-failure (Site not responding. Last check: 2007-10-15)
		The interaction of negation as failure and the depth-bound is handled correctly.
		The interaction of negation as failure with assumables isn't satisfactory.
		It is recommended that you don't use both assumables and negation as failure.
	www.cs.ubc.ca /spider/poole/ci/code/cilog/cilog_man_15.html (79 words)

	Negation as failure - Wikipedia, the free encyclopedia
		Negation as failure is an interpretation of logical negation according to which the negation of a formula is true if and only if the formula cannot be proved true.
		Negation as failure is used in logic programming languages such as Prolog.
		Negation as failure is related to the common default assumption that what is not known to be true is false.
	en.wikipedia.org /wiki/Negation_as_failure (259 words)

	Support LP semantics with negation as failure and strong negation - W3C RIF-WG Wiki (Site not responding. Last check: 2007-10-15)
		Negation as failure --- more accurately called "default negation" --- has been the staple of logic programming and databases for over 20 years.
		Default negation means that a fact is declared false if it cannot be proven true.
		The semantics of such negation has been worked out in the LP and DB commmunities in the late 80's and currently two semantics are widely used: the well-founded semantics and the stable-model semantics.
	www.w3.org /2005/rules/wg/wiki/Support_LP_semantics_with_negation_as_failure_and_strong_negation (181 words)

	Negation in XSB
		Negation in the context of logic programming has received a lot of attention.
		So to guarantee reasonable answers to queries to programs containing negation, the negation operator must be allowed to apply only to ground literals.
		The other problem that may arise in programs with negation, that of nonstratification, is a bit more subtle.
	www.cs.sunysb.edu /~warren/xsbbook/node58.html (655 words)

	negation - W3C RIF-WG Wiki (Site not responding. Last check: 2007-10-15)
		In the ongoing discussion about monotonic vs. non-monotonic negation (better known as negation as failure), it is often overlooked that not only non-monotonicity is an issue but actually there are several definitions of both monotonic and non-monotonic forms of negation in the literature) with subtle but important differences.
		This overview is by no means to be understood to be exhaustive, but shall cover and clarify the most prominent forms of negation in the context of logics and rule languages, especially those mentioned in discussions within the RIF working group.
		Constructive negation (due to Nelson in 1949) adds to intuitionistic logic the insight that primitive propositions may not only be constructively verified but also be constructively falsified.
	www.w3.org /2005/rules/wg/wiki/negation (1873 words)

	20th WCP: Abduction and Hypothesis Withdrawal in Science
		There is a kind of negation, studied by researchers into logic programming, which I consider to be very important also from the epistemological point of view: negation as failure.
		Contrasted with classical negation, with the double negation of intuitionistic logic, and with the philosophical concept of Aufhebung, negation as failure shows how a subject can decide to withdraw his hypotheses, while maintaining the rationality of his reasoning, in contexts where it is impossible to find contradictions and anomalies.
		In (Magnani, 1991 e 1997b) I have explored whether negation as failure can be employed to model hypothesis withdrawal in Poincare's conventionalism of the principles of physics, showing how conventions can be motivationally abandoned.
	www.bu.edu /wcp/Papers/Scie/ScieMagn.htm (3004 words)

	Charles Young : Negation-as-Failure and the Microsoft Business Rules Engine (Site not responding. Last check: 2007-10-15)
		Negation can be a surprisingly problematic issue in the world of rules.
		Sometimes, it is desirable to treat the failure to evaluate the truth value of a proposition as a negation of the proposition being tested.
		This article has attempted to explain the notion of Negation as Failure, and to show why direct support for it in a rules engine is welcome.
	blog.solidsoft.com /blogs/charles_young_mvp_biztalk/archive/2006/10/16/149.aspx (2632 words)

	Nonmonotonic Reasoning and Modal Logic (Site not responding. Last check: 2007-10-15)
		The epistemological properties of Lifschitz's logic of minimal knowledge and negation as failure MKNF are investigated in [212].
		Such a complexity characterization induces a complexity based classification of the various forms of nonmonotonic reasoning considered: in particular, it is proven that negation as failure is computationally harder than epistemic disjunction, which apparently contradicts previous complexity results obtained in the logic programming setting.
		In [215, 214] a unifying view of negation as failure, integrity constraints, and epistemic queries in nonmonotonic reasoning is presented.
	www.dis.uniroma1.it /common/rappric/rappric98/node65.html (756 words)

	[No title]
		NAF is the most commonly used form of negation in commercially important rule systems, i.e in Prolog, SQL, OPS5 production rules, ECA rules.
		More precisely, body atoms may have a NAF operator appear immediately before them, in which case they are interpreted as a NAF negative literal.
		The semantics of negation-as-failure gets a bit complicated, however, when it interacts with recursive/cyclic dependencies among predicates/literals, since in general there may be oscillatory ill-definedness of whether a cyclically-dependent literal is to be entailed as in or out of the model (i.e., conclusion set).
	www.daml.org /listarchive/joint-committee/att-1336/01-negation-approach-msg1-v12.txt (493 words)

	Negation in CycL
		In general, the failure to prove P is not a sound basis for concluding (not P), i.e., that P is false.
		Nevertheless, it is sometimes useful to permit this conclusion to be tentatively drawn.
		would indicate that we will use the failure to prove P as a weak argument for P whenever the predicate is #$geographicalSubRegions.
	www.cyc.com /cycdoc/ref/negation.html (774 words)

	Embedding negation as failure into minimal knowledge (Site not responding. Last check: 2007-10-15)
		In this paper we prove that it is possible to express negation as failure in terms of minimal knowledge.
		Specifically, we present a polynomial, non-faithful, modular embedding of Lifschitz's logic of minimal knowledge and negation as failure MKNF into Halpern and Moses' logic of minimal knowledge S5G.
		From the theoretical viewpoint, this result implies that minimal knowledge has the same expressive power of negation as failure, hence it is possible to embed all the best known propositional nonmonotonic formalisms, in particular default logic, autoepistemic logic, and circumscription, into S5G.
	www.dis.uniroma1.it /~rosati/publications/Rosa98b.htm (210 words)

	Citations: An extension of explanation-based generalisation to negation as failure - Schrodl (ResearchIndex)
		Citations: An extension of explanation-based generalisation to negation as failure - Schrodl (ResearchIndex)
		An extension of explanation-based generalisation to negation as failure.
		....of Failures (EBGF) A sufficient condition is derived from the failed proof tree which is satisfied by the instance and ensures the failure of the goal.
	citeseer.ist.psu.edu /context/785897/0 (314 words)

	Reasoning about Minimal Belief and Negation as Failure
		, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming.
		Among the nonmonotonic modal logics proposed in the literature, the logic of minimal belief and negation as failure
		is the true logic of negation as failure (as interpreted according to the stable model semantics).
	www.cs.cmu.edu /afs/cs/project/jair/pub/volume11/rosati99a-html/rosati99a-html.html (3798 words)

	OE Handbook: Chapter 14. Using CycL Queries
		Enabling negation by failure allows the inference engine to prove the negation of certain assertions when it fails to prove those assertions themselves.
		When negation by failure is enabled, and one asks the negation of a closed formula FORM in which the arg0 is a predicate PRED such that (#$minimizeExtent PRED) is true in a microtheory accessible to the microtheory in which the query is made, then the inference engine will return 'True' if it cannot prove FORM.
		Since negation by failure allows us to assume that the negation of an assertion is true when the assertion itself cannot be proven, it is best used in those situations in which such an assumption is plausible, or, alternatively, in situations in which one wishes to test the plausibility of such an assumption.
	www.cyc.com /doc/handbook/oe/14-using-cycl-queries.html (5837 words)

	A FIXPOINT THEOREM IN LINEAR LOGIC
		for negation there is nothing similar ; moreover the fact that proof-search ignores contraction renders the behaviour of negation by failure absolutely non-classical.
		What actually happens is that one only looks for arbitrary fixpoints in NAF, but since we are interested in provability, what holds is what is true in all these fixpoints (hence in the smallest one if any).
		In fact the usual definition states that int is the smallest closed set, and one must PROVE that it is actually a fixpoint ; this proof is the linear time algo for predecessor.
	www.cis.upenn.edu /~bcpierce/types/archives/1992/msg00030.html (1524 words)

	Seminars and Events: SFU Computing Science (Site not responding. Last check: 2007-10-15)
		In fact, there is no single method with this characteristic (for instance, negation as failure is incomplete, while constructive negation is hard to implement and until our work there were no running implementation of it).
		In this talk I will present a novel method for incorporating negation into a Prolog compiler which takes a number of existing methods (some modified and improved by us) and uses them in a combined fashion.
		In this talk constructive negation is oriented to the implementation issues, and its practical applications.
	www.cs.sfu.ca /news/index.cgi/events/2006-07-17-1.html (249 words)

	Production Systems Need Negation as Failure (Site not responding. Last check: 2007-10-15)
		We study action rule based systems with two forms of negation, namely classical negation and ``negation as failure to find a course of actions''.
		We show by several examples that adding negation as failure to such systems increase their expressiveness, in the sense that real life problems can be represented in a natural and simple way.
		Then, we address the problem of providing a formal declarative semantics to these extended systems, by adopting an argumentation based approach, which has been shown to be a simple unifying framework for understanding the declarative semantics of various nonmonotonic formalisms.
	www.di.unipi.it /~paolo/abstracts/aaai96.abstract.html (148 words)

	COMPUTER SCIENCE TECHNICAL REPORT ABSTRACTS (Site not responding. Last check: 2007-10-15)
		Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation from Horn logic to a fragment of higher-order hereditary Harrop formulae.
		This can be seen as a negation normal form procedure which is consistent with intuitionistic provability.
		As this is in general not possible, we restrict ourselves to a fragment in which clause complementation is viable and that has proven to be expressive enough for the practice of logical frameworks.
	reports-archive.adm.cs.cmu.edu /anon/2000/abstracts/00-175.html (233 words)

	Adding Negation-as-Failure to Intuitionistic Logic Programming - Bonner, McCarty (ResearchIndex)
		negation as failure (Section 5) In contrast, adding negation as failure to intuitionistic logic is problematic, as pointed out in [32] and
		0.3: Hypothetical Datalog: Negation and Linear Recursion - Bonner (1989)
		9 Hypothetical Datalog: Negation and Linear Recursion - Bonner - 1989 DBLP
	citeseer.ist.psu.edu /bonner92adding.html (620 words)

	10.3 Negation as failure
		By working with negation as failure (instead of with the lower level cut-fail combination) we have a better chance of avoiding the programming errors that often accompany the use of red cuts.
		In fact, negation as failure is so useful, that it comes built in Standard Prolog, we don't have to define it at all.
		Summing up, we have seen that negation as failure is not logical negation, and that it has a procedural dimension that must be mastered.
	www.coli.uni-saarland.de /~kris/learn-prolog-now/html/node90.html (948 words)

	Answer set programming - Wikipedia, the free encyclopedia
		In traditional logic programming, negation-as-failure indicates the failure of a derivation; in answer set programming, it indicates the consistency of assumption of falsehood of a literal.
		It should be noted though, that in the propositional case (as it is the case in answer set programs) these two interpretation of negation (as failure) coincide.
		A literal is either an atom or a negated (using classical negation) atom.
	en.wikipedia.org /wiki/Answer_set_programming (698 words)

	Negation and Control
		Further discussion of conditions allowing cuts and of their actions can be found in Section 5.1.
		must be ground for sound negation as failure, although no runtime checks are made by the system.
		must be ground for sound negation, although no runtime checks are made by the system.
	www.cs.sunysb.edu /~sbprolog/manual1/node74.html (246 words)

	CS312 -- Negation (Site not responding. Last check: 2007-10-15)
		But we are working with Horn clauses, and we cannot have negated rule heads.
		We cannot use NAF as it is. We cannot tell, in general, whether a goal
		Negated goals must be ground for negation as failure in Prolog to work correctly.
	www.cse.buffalo.edu /faculty/alphonce/.OldPages/CPSC312/CPSC312/Lecture/LectureHTML/CS312_8.html (307 words)

	joint-committee Mailing List Archive: markup tagnames for negation: consensus formulation and notes from RuleML SC ...
		2 years ago to have this taxonomy: not (neutral, NL-oriented) neg (strong, technical) naf (nonmon, technical) This was also reflected in: http://www.daml.org/listarchive/joint-committee/1077.html In the SC we decided mid-Sep to go with neg (for classical-strong), as mentioned in my editing suggestions to Peter (which he implemented).
		Here it is: In markup tags: neg stands for classical negation in FOL, strong negation in LP naf stands for negation-as-failure, a.k.a.
		weak negation and default negation Often in a given tool-specific rule/KB editors' presentation syntax/view, however, one could without ambiguity use "not" for negation, because only one form of negation would be available.
	www.daml.org /listarchive/joint-committee/1826.html (605 words)

	Ordered Logic Program Solver (Site not responding. Last check: 2007-10-15)
		Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones.
		We equip ordered logic programs with negation as failure, using a simple generalization of the preferred answer set semantics for ordered programs.
		Interestingly, allowing negation as failure in ordered logic programs does not yield any extra computational power: the combination of negation as failure and order can be simulated using order (and true negation) alone.
	tinf2.vub.ac.be /olp (1237 words)

	Production Systems with Negation as Failure (Site not responding. Last check: 2007-10-15)
		Then, we address the problem of providing a formal declarative semantics to these extended systems, by adopting an argumentation based approach, which has been shown to be a simple unifying framework for understanding the declarative semantics of various non-monotonic formalisms.
		Next, we characterize the class of stratified production systems, which enjoy the properties that the above mentioned semantics coincide and that negation as failure to find a course of actions can be computed by a simple bottom-up operator.
		Stratified production systems can be implemented on top of conventional production systems by compiling away negation as failure.
	www.di.unipi.it /~paolo/abstracts/tkde.abstract.html (187 words)

	Closed world assumption - Wikipedia, the free encyclopedia
		Negation as failure is related to the closed world assumption, as it amounts to believe false every predicate that cannot be proved to be true.
		In all cases, the formalization of the closed world assumption is based on adding to K the negation of the formulae that are “free for negation” for K, i.e., the formulae that can be assumed to be false.
		The set F of formulae that are free for negation in K can be defined in different ways, leading to different formalizations of the closed world assumption.
	en.wikipedia.org /wiki/Closed_World_Assumption (681 words)

	MS BRE: Negation-as-Failure and the Microsoft Business Rules Engine
		The main issue we had was the lack of support for negated conjunction.
		More importantly, the work we did suggest that Miss Manners does little more than measure negated conjunction at a single node, which is one more reason why it is a poor choice as a general purpose comparative benchmark.
		‘Negation’ refers to any mechanism by which we change the truth value of a statement to the opposite...
	geekswithblogs.net /cyoung/articles/90100.aspx (4259 words)

	Prolog Tutorial -- 2.5 (Site not responding. Last check: 2007-10-15)
		The definition of program clause tree in previous sections was intended for programs without negation as failure.
		For programs having negation as failure in the bodies of program clauses, the definition of a program clause tree, and the definition of a consequence based upon these trees needs to be carefully formulated.
		The last two exercises show that programs with negation as failure can be problematic if there is either recursion through negation or if the negation of some unbounded literal is considered.
	www.csupomona.edu /~jrfisher/www/prolog_tutorial/2_5.html (487 words)

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