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Topic: Default logic

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	Non-monotonic Logic (Stanford Encyclopedia of Philosophy)
		Pioneering work in the field of non-monotonic logics began with the realization that ordinary first-order logic is inadequate for the representation of defeasible reasoning accompanied by the effort to reproduce the success of FOL in the representation of mathematical, or formal, reasoning.
		Default logic is intimately connected with certain modal approaches to non-monotonic reasoning, which belong to the family of autoepistemic logics.
		Modal logics in general have proved to be one of the most flexible tools for modelling all sorts of dynamic processes and their complex interactions (see the entry "modal logic", this Encyclopedia).
	plato.stanford.edu /entries/logic-nonmonotonic (6364 words)

	Default logic
		Default logic is a non-monotonic logic proposed by Ray Reiter to formalize reasoning with default assumptions.
		The logical formulae in W and all formulae in a default were originally assumed to be first-order logic formulae, but they can potentially be formulae in an arbitrary formal logic.
		This variant of default logic is related in principles to autoepistemic logic, where a theory has the model in which x is true just because, assuming true, the formula supports the initial assumption.
	www.brainyencyclopedia.com /encyclopedia/d/de/default_logic.html (2101 words)

	Default Logic Simulation
		This is a Java-applet to visualize the calculation of extensions for default theories in Default Logic, a special logic to represent uncertain (or "default") knowledge.
		This logical formalism has been introduced by Reiter in 1980 (Reiter, R., A Logic for Default Reasoning.
		This is a lecture for advanced students of computer science and logic.
	www.kr.tuwien.ac.at /students/dls/english/index.html (160 words)

	default_logic - The Wordbook Encyclopedia
		Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions.
		This variant of default logic is related in principle to autoepistemic logic, where a theory
		Statistical variant : a statistical default is a default with an attached upper bound on its frequency of error; in other words, the default is assumed to be an incorrect inference rule in at most that fraction of times it is applied.
	www.thewordbook.com /default_logic (1632 words)

	Logic and Artificial Intelligence (Stanford Encyclopedia of Philosophy)
		The other varieties of nonmonotonic logic, including default logic and the modal nonmonotonic logics, raise issues of the sort that are familiar to philosophical logicians, having to do with the design of new logics, the systematic investigation of questions concerning validity, and managing the proliferation of alternative logics.
		The idea of a logic of tense in the modern sense has been familiar since at least the work of Jan Łukasiewicz (see, for instance, Łukasiewicz 1970), but the shape of what is commonly known as tense logic was standardized by Arthur Prior's work in the 1950s and 1960s: see Prior 1956, 1967, 1968.
		Priorian tense logic shares with modal logic a technical concentration on issues that arise from using the first-order theory of relations to explain the logical phenomena, an expectation that the important temporal operators will be quantifiers over world-states, and a rather distant and foundational approach to actual specimens of temporal reasoning.
	plato.stanford.edu /entries/logic-ai (16977 words)

	Default logic - Definition, explanation
		Default logic is a non-monotonic logic proposed by Ray Reiter to formalize the way humans reason using default assumptions.
		The computer language Prolog uses a sort of default assumption when leading with negatation: if a negative atom cannot be proved to be true, then it is assumed to be false.
		A default theory in which all defaults are normal is guaranteed to have at least one extensions.
	www.calsky.com /lexikon/en/txt/d/de/default_logic.php (745 words)

	Default logic - Wikipedia, the free encyclopedia
		Default logic is a non-monotonic logic proposed by Ray Reiter to formalize reasoning with default assumptions.
		The logical formulae in W and all formulae in a default were originally assumed to be first-order logic formulae, but they can potentially be formulae in an arbitrary formal logic.
		a statistical default is a default with an attached upper bound on its frequency of error; in other words, the default is assumed to be an incorrect inference rule in at most that fraction of times it is applied.
	en.wikipedia.org /wiki/Default_logic (2009 words)

	DeReS
		Default logic was introduced by Reiter in 1980 as a tool for reasoning based on incomplete information.
		The progress in understanding of the theory of default logic has been reflected in the development of algorithms for computing default extensions, as well as in first implementation projects.
		This can be accomplished through the development of much faster than presently available implementations of default logic, through the systematic studies and development of the methodology of programming with default logic, through comprehensive experimentation and by demonstrating usefulness of default logic as a computational mechanism for AI applications.
	www.cs.engr.uky.edu /~mirek/computing-with-dl.html (500 words)

	Citations: An Introduction to Default Logic - Besnard (ResearchIndex)
		In default logic, knowledge is represented as a default theory, which consists of a set of first order formulae and a set of default rules for representing default information.
		The default and the autoepistemic logics were designed to model commonsense forms of reasoning, in particular, reasoning patterns of the form in the absence of any information to the contrary infer.
		A default theory is then a pair W, D where W is a set of sentences (the axioms of) and D a set of default rules.
	citeseer.ist.psu.edu /context/37814/0 (2234 words)

	logic_programming
		For example, the relation between priority and default is investigated deeply in a number of papers by Dr. You and his colleagues at University of Alberta.
		This is because (i) priority is in general a nonmonotonic language construct; (ii) positive logic programming with constraints assumes the availability of constraint solvers for the underlying constraint problems; and (iii) constraint predicates cannot appear in the head of a clause due to the mechanism of embedding.
		Since the translated logic programs are a specific class of logic programs, their properties will be studied, which could be used to simplify and improve the logic programming procedures.
	www.cs.ualberta.ca /~you/Research/constraint-lp.html (2489 words)

	Book review of Matthew Ginsberg
		McDermott's formulation of modal logic (1980) is based on a coherence operator ("P is coherent with what is known" if P cannot be proven false by what is known).
		Moore's "Semantical consideration of nonmonotonic logic" (1985) removed some of the problems with McDermott's with his "autoepistemic logic", based on the notion of belief (related to McDermott's coherence), which extends Hintikka's epistemic modal logic to incorporate action.
		Circumscription deals with default inference by minimizing abnormality: an axiom that states what is abnormal is added to the theory of what is known (predicate circumscription).
	www.thymos.com /mind/ginsberg.html (918 words)

	Default Logic
		The idea is to reason in first order logic but to have available a set of default rules which are used only if an inference can not be obtained within the first order formulation.
		Default theory is an attempt to formally capture the idea that a set of beliefs may permit certain conclusions to be drawn even though these conclusions are not logically implied by the current set of beliefs.
		This default rule is applicable if we can prove from our beliefs that John is an American and an adult, and believing that there is some car that is owned by John does no't lead to an inconsistency.
	www.rci.rutgers.edu /~cfs/472_html/Logic_KR/DefaultTheory.html (456 words)

	Many-valued logic processor for data query systems - Patent 5398199
		In fact, various alternative logic semantics can be supported and can be selected for the query processing; the application software adjusts the selection condition to the logic selected by the user or, in lack of a user specification, to the logic designated by the system developer as the default logic.
		For the n-valued logics currently reported in the literature, any n, the number of bits of truth value code is n-1, that is, it equals the number minus one of truth values of that logic.
		As to b-circuit-1 930, AND gate 931 performs the logical and between signals 901 and 911, and its output signal 932 is applied to the lower input of XOR gate 933.
	www.freepatentsonline.com /5398199.html (10397 words)

	Citations: An alternative semantics for default logic - Guerreiro, Casanova (ResearchIndex)
		and the i least fixpoint of the stable operator E st Delta for E Delta yields the well founded semantics for default logic described in (Baral and Subrahmanian, 1991) The semantics landscape of default logic is depicted in Figure 1.
		and the i least xpoint of the stable operator C E for E yields the well 18 founded semantics for default logic described by Baral and Subrahmanian in (Baral and Subrahmanian, 1991) The semantics landscape of default logic is depicted in Figure 1.
		and the i least fixpoint of the stable operator C E Delta for E Delta yields the well 18 founded semantics for default logic described by Baral and Subrahmanian in (Baral and Subrahmanian, 1991) The semantics landscape of default logic is depicted in Figure 1.
	citeseer.ist.psu.edu /context/210914/0 (845 words)

	Inductive versus Fixpoint Definitions in Default Logic and Logic Programming
		In classical logic, the notion of a derivation is defined inductively, as also in most non-classical logics.
		But in default logic and nonmonotonic logic programming with the answer-set semantics, induction is abandoned in favour of extensions understood as fixpoints.
		Nevertheless, Brewka (1994) showed that in Reiter default logic with normal rules we may replace fixpoint definitions by inductive ones; and the procedural presentation of non-normal Reiter default systems by Antoniou (1997) in effect implies the same for them too.
	www.cse.unsw.edu.au /research/seminars/ai/makinson.html?printable=yes (521 words)

	CrunchyLogic (Site not responding. Last check: 2007-11-06)
		Thus in traditional default logic, there are two extensions; one where Nixon is a pacifist (since we follow (1)) and one where Nixon is not a pacifist (since we follow (2)).
		While we might accept the plausibility of the default about the decision to buy stocks, such new information still undercuts its conclusion–that we should buy E Inc. stocks–since we have good reason to believe the rule’s prerequisite is untrue.
		The driving force for default rules is the assumption that in our incomplete knowledge, we may still arrive at conclusions which are plausible, but not classically provable from our initial knowledge of the world.
	www.underlevel.net /crunchylogic (4443 words)

	Selected Publications
		A paper coauthored with A. Nerode and J. Remmel on complexity of normal default logic.
		An unpublished paper coauthored with A. Nerode on a decision procedure for Default Logic of Reiter.
		A paper coauthored with M. Truszczynski on the interpretation of default logic in nonmonotonc pure logic of necessitation.
	www.cs.engr.uky.edu /~marek/papers.dir/papersvm.html (2327 words)

	Default - Wikipedia, the free encyclopedia
		To default in tennis is to fail to participate in or complete a match; for example, due to an injury.
		If a player defaults, the opponent is considered to have won the match.
		defaults (software) is the utility that manipulates Mac OS X plist (preference) files.
	en.wikipedia.org /wiki/Default (137 words)

	Bibliography
		Anderson, A reduction of deontic logic to alethic modal logic, Mind 67 (1958), 100-103.
		Levesque, A logic of implicit and explicit belief, Proceedings AAAI-84 (Austin, TX), 1984, pp.
		Meyer, A logic of capabilities (extended abstract), Proceedings of the Third International Symposium on the Logical Foundations of Computer Science (LFCS'94) (A. Nerode and Yu.V. Matiyasevich, eds.), LNAI, vol.
	stinfwww.informatik.uni-leipzig.de /~duc/Thesis/node58.html (1448 words)

	Expressing Default Logic Variants in Default Logic -- Delgrande and Schaub 15 (5): 593 -- Journal of Logic and ...
		Reiter's default logic is one of the best known and most studied
		logic can be expressed in rational default 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.
	dx.doi.org /10.1093/logcom/exi021 (342 words)

	Citebase - Representation Theory for Default Logic
		Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent.
		In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory.
		We construct examples of denumerable families of non-including theories that are not representable.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:cs/9901016 (151 words)

	Answer Record # 15786: 9.1i PACE - A default area group is not large enough to fit logic, causing MAP to report errors
		A default area group is not large enough to fit logic, which causes errors in MAP.
		PACE defaults to a 25% area group padding estimation during a drag-and-drop operation.
		If the unrelated logic packing indicated by the MAP report is not full, manually modify the UCF to increase the area group compression factor.
	www.xilinx.com /xlnx/xil_ans_display.jsp?BV_UseBVCookie=yes&getPagePath=15786&iLanguageID=1 (337 words)

	Digital Logic
		Logic example of Doors Opening and Closing, you can see that in order for the "Light" to get through the house, the front door AND the back door must be Open.
		Logic example, you can see that in order to get light through the house: the left front door OR the right front door (or both) must be Open.
		The convention (which is not always adhered to) is that a POSITIVE Gate Inversion is indicated by a bubble on the output, and with Negative logic the bubble is at the input.
	www.williamson-labs.com /480_logic.htm (666 words)

	ConditionalInterceptor (Jive Forums API (5.5.7) Developer Javadocs)
		Constant to indicate the interceptor logic should be invoked after passing control down the interceptor chain.
		Constant to indicate the interceptor logic should be invoked before passing control down the interceptor chain.
		Additionally, the logic may be skipped depending on the allow or disallow rules.
	www.jivesoftware.com /builds/docs/latest/documentation/javadoc/dev/com/jivesoftware/base/action/interceptor/ConditionalInterceptor.html (451 words)

	Journal of the ACM Bibliography (Site not responding. Last check: 2007-11-06)
		All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundedness-conditions.
		Hence, the question naturally arises whether default logic can be translated into standard AEL at all.
		However, we are able to construct a faithful polynomial-time translation from default logic into standard AEL which is nonmodular.
	theory.lcs.mit.edu /~jacm/References/gottlob1995:711.html (239 words)

	Basic PowerLoom Commands
		Each ;; demo file uses its own module to avoid interference with other ;; demos (all demo modules are organized as siblings which have ;; `PL-USER' as their common parent module).
		DEMO: Read logic commands from a file, echo them verbatimly to standard output, and evaluate them just as if they had been typed in interactively.
		From the logic point-of-view, every slot ;; is a (polymorphic) function or binary relation that could have been ;; defined alternatively with `deffunction' or `defrelation'.
	www.isi.edu /isd/LOOM/PowerLoom-work/documentation/examples/basics.html (1505 words)

	A structural property on modal frames characterizing default logic
		Modal logics characterized by a class of frames satisfying the insertion property are shown to be suitable for Reiter's default logic.
		The canonical fix point construction defined by Marek, Schwarz and Truszczynski for Reiter's default logic is refined and a new paradigm for nonmonotonic logic is addressed.Suitable modal logics for such a construction must contain KD4.
		When reflexivity is added to the modal logic used for the fix point construction then the Marek Schwarz and Truszczynski framework for Reiter's default logic is obtained.
	www.dis.uniroma1.it /~ai/citations/amat-etal-96b.html (227 words)

	Logic Resources
		My Gateway to Logic displays truth tables, expression trees, alpha graphs, normal forms and so on, both in a server side and a client side version.
		Metamath Solitaire is a Java applet that allows to interactively construct proofs in predicate logic and set theory; it uses an axiomatic approach.
		John Kennedy's Propositional Logic Program displays truth tables and expression trees, converts propositions to Polish notation and optimizes using the algorithm of Karnaugh/Veitch.
	logik.phl.univie.ac.at /~chris/logic.html (370 words)

	eZ Systems - Phil. Fakultaet - Probabilistic Default Logic Based on Relevance - ...
		Fakultaet - Probabilistic Default Logic Based on Relevance -...
		This paper embeds default logic into an extension of Adams’ probability logic, called the system P+ DP.
		Default reasoning is furnished with two mechanisms: one generates (ir)relevance assumptions, and the other propagates lower probability bounds.
	thphil.phil-fak.uni-duesseldorf.de /index.php/article/view/54/1/14 (80 words)

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