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Topic: Monotonicity of entailment

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	Monotonicity of entailment - Wikipedia, the free encyclopedia
		Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions.
		In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment if monotone just in case the rule is admissible.
		Logical systems with this property are occasionally called monotonic logics in order do differentiate them from non-monotonic logics.
	en.wikipedia.org /wiki/Monotonicity_of_entailment (181 words)

	Articles - Monotonic (Site not responding. Last check: 2007-10-22)
		In mathematics, functions between ordered sets are monotonic (or monotone, or even isotone) if they preserve the given order.
		Inspired by the shape of the graph of a monotone function on the reals, such functions are also called monotonically increasing (or "non-decreasing" or, less precisely, just "increasing").
		A constant function is both monotone and antitone; conversely, if f is both monotone and antitone, and if the domain of f is a lattice, then f must be constant.
	www.centralairconditioners.net /articles/Monotonic (809 words)

	RDF Semantics
		Through the notions of satisfaction, entailment and validity, formal semantics gives a rigorous definition to a notion of "meaning" that can be related directly to computable methods of determining whether or not meaning is preserved by some transformation on a representation of knowledge.
		Simple interpretations and simple entailment capture the semantics of RDF graphs when no attention is paid to the particular meaning of any of the names in the graph.
		All of these additions are monotonic, in the sense that entailments which hold before the addition of information, also hold after it.
	www.w3.org /TR/rdf-mt (11716 words)

	[No title]
		Entailment with respect to these selected models is referred to as filter entailment.
		We extend the notions of abductive reasoning and filter entailment to allow preferences among explanations and models respectively and give conditions when they are equivalent.
		The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches.
	www.cs.utep.edu /chitta/papers/abstracts.html (2408 words)

	_____V.3
		All the fundamental components of a logic like those of syntax, entailment system, models, proof calculus and satisfaction are included in the definition of a (general) logic.
		Entailment systems is a categorical formalization of the broad concept of (syntactical) Logical context for theories.
		The entailment system approach is invariant of the choice of initial concepts (called signatures) and of the way the propositions are composed (category of sentences).
	www.softlab.ntua.gr /~kyritsis/PapersInComputerScience/6BARCEL9.htm (1054 words)

	Abstracts Linguistics Meetings - Spring 2000
		Groenendijk and Stokhof (1997) suggest that entailment relations should also be taken as driving the semantics of questions.
		One of the approaches to natural language semantics states that what we are interested in is an ability to explain and predict entailments between sentences in natural language and not only the meaning of specific sentences per se.
		Entailment between sentences is viewed as a partial order relation that can be calculated from orders between sub-sentential expressions.
	www.cs.technion.ac.il /~winter/ling/abstracts.html (1321 words)

	RDF Semantics
		MUST define a notion of vocabulary entailment which is valid according to the model-theoretic semantics described in the normative parts of this document; except that if the semantic extension is defined on some syntactically restricted subset of RDF graphs, then the semantic conditions need only apply to this subset.
		Simple interpretations and simple entailment capture the semantics of RDF graphs when no attention is paid to the particular meaning of any of any of the names in the graph.
		However, it will usually not be appropriate to consider such 'trivial' entailments as useful consequences, since they may not be valid entailments in a smaller vocabulary.
	www.w3.org /TR/2003/WD-rdf-mt-20031010 (11637 words)

	Abstract (Site not responding. Last check: 2007-10-22)
		Negative polarity item licensing (1-4) and entailment patterns (6-8) indicate that certain adjectives generate monotone decreasing contexts, while others generate monotone increasing contexts (cf.
		Monotonicity properties represent one of several factors which have traditionally been used to classify gradable adjectives according to their "logical polarity" (in the sense of H. Klein 1996).
		Adjectives which license negative polarity items and downward entailments in clausal complements, such as difficult and strange, are classified as "negative", while adjectives which do not license negative polarity items but do permit upward inferences, such as easy and common, are classified as "positive" (see Seuren 1978 for early discussion of this issue).
	home.uchicago.edu /~ck0/docs/monotonicity.html (206 words)

	RDF Semantics
		Model theory is usually most relevant to implementation via the notion of entailment, described later, which makes it possible to define valid inference rules.
		SHOULD be indicated by the use of a vocabulary entailment term.
		This follows the wording of the definition of simple entailment in Section 2, but refers only to rdfs-interpretation s instead of all simple interpretations.
	lists.w3.org /Archives/Public/www-rdf-comments/2004JanMar/att-0033/sempr-sem2004a.html (10362 words)

	RDF Semantics
		All but one of the RDFaxiomatic triples can be derived from the rules rdfs2 and rdfs3 and the RDFS axiomatic triples, for example; and rule rdfs1 subsumes cases of rule se1 where vvv is a plain literal.
		The stronger extensional semantic conditions described in Section 4.1 sanction further entailments which are not covered by the RDFS rules.
		In order to capture datatype entailment in terms of assertions and entailment rules, the rules need to refer to information supplied by the datatypes themselves; and to state the rules it is necessary to assume syntactic conditions which can only be checked by consulting the datatype sources.
	lists.w3.org /Archives/Public/www-archive/2003Jul/att-0035/semantics-2003-07-29.html (11657 words)

	v
		The idea is to “unfold” the category of deductions of the entailment to one that is actually the universal covering tree of them.
		And any morphism between the derived entailment systems is projected directly to a morphism of the source entailment systems.And in addition any morphism of the two entailment systems E
		Theorem 4.7 There is forgetfull functor from the category of entailment systems E with arrows the covering maps, to the category of topological spaces (actually realisations of graphs).
	www.softlab.ntua.gr /~kyritsis/PapersInComputerScience/6BARCEL9.html (3782 words)

	Logic - Wikipedia, the free encyclopedia
		The second class of paradoxes involves redundant premises, falsely suggesting that we know the succedent because of the antecedent: thus "if that man gets elected, granny will die" is materially true if granny happens to be in the last stages of a terminal illness, regardless of the man's election prospects.
		Such sentences violate the Gricean maxim of relevance, and can be modelled by logics that reject the principle of monotonicity of entailment, such as relevance logic.
		Closely related to questions arising from the paradoxes of implication comes the radical suggestion that logic ought to tolerate inconsistency.
	en.wikipedia.org /wiki/Formal_logic (4670 words)

	Defeasible Reasoning
		Deductive consequence is monotonic: if a set of premises logically entails a conclusion, than any superset (any set of premises that includes all of the first set) will also entail that some conclusion.
		Somewhat surprisingly, Pollock assumes a principle of monotonicity with respect to hypotheses: a belief that is warranted relative to a set of hypotheses is also warranted with respect to any superset of hypotheses.
		The one critical drawback to Commonsense Entailment, when compared to the logic of extreme probabilities, is that it lacks a single, clear standard of normativity.
	plato.stanford.edu /entries/reasoning-defeasible (12385 words)

	Monotonicity Of Entailment (Site not responding. Last check: 2007-10-22)
		Please look for Monotonicity Of Entailment, High School Math Worksheets and Free Algebra Worksheets to find more Monotonicity Of Entailment information.
		Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended...
		Monotonicity of entailment - RecipeFacts Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any...
	www.monotonicityofentailment.info (257 words)

	SICStus Prolog User's Manual - Constraint Logic Programming over Finite Domains (Site not responding. Last check: 2007-10-22)
		If a constraint is reified, the definition must contain four clauses for solving and checking entailment of the constraint and its negation.
		The indexicals must be monotone before they are admitted for execution.
		When a constraint is reified, the solver spawns two reactive agents corresponding to detecting entailment and disentailment.
	www.cl.cam.ac.uk /ailanguages/sicstus3.5/sicstus_32.html (4428 words)

	Inductive Logic
		In a valid deductive argument the premises logically entail the conclusion, where such entailment means that the truth of the premises provides a guarantee of the truth of the conclusion.
		The idea was to extend the deductive entailment relation to a notion of probabilistic entailment for cases where premises provide less than conclusive support for conclusions.
		The notion of logical entailment is interdefinable with it.
	plato.stanford.edu /entries/logic-inductive (12775 words)

	[No title]
		Even if the languages used for encoding knowledge in different domains are special purpose (like action languages) we will not have any problem combining them together if their entailment relations are formalized in the same language.
		Suppose you have some collection of actions and their effects and would like to write a planner which examines, in some reasonable order, possible sequences of actions and checks if your domain description entails that the goal G holds after the sequence of actions is executed.
		The corresponding logic programming formalization of this entailment together with the domain description forms the main part of the planner.
	www.ida.liu.se /ext/etai/actions/nj/9711-2/inbody.html (7436 words)

	Notes
		It also covers entailment, causality, consequence, induction, deduction, truth, falsity, belief, fallacies, paradoxes, probabilities, analysis, tense, modality, necessity, sufficiency, possibility, justification, tolerance, obligation, permission, relevance, assertion, validity, contradiction, provability, and argumentation.
		A non-monotonic logic rejects the monotonicity of entailment.
		If a logic is monotonic, then adding new information can change the set of known facts, causing previously known truths to become falsehoods.
	www.technocage.com /~ray/notespage.jsp?pageName=logic&pageTitle=Logic (1195 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		We address the problem by defining the notion of coclosure under co-Horn rules, that can be used to remedy violation of certain rules by removing arguments.
		In particular, we show how the coclosure under Monotonicity can be used to construct the monotonic restriction of a preferential relation.
		A salient feature of this framework is that it is also possible to compare rule systems that are not related by metalevel entailment.
	tennessee.cc.vt.edu /~akrowne/citidel/export/ri_ncstrl_dump/OAI.CITIDEL_RI.3502.txt (160 words)

	Papers by Bill MacCartney
		Current approaches to semantic inference in question answering and textual entailment have approximated the entailment problem as that of computing the best alignment of the hypothesis to the text, using a locally decomposable matching score.
		Instead we propose a pipelined approach where alignment is followed by a classification step, in which we extract features representing high-level characteristics of the entailment problem, and pass the resulting feature vector to a statistical classifier trained on development data.
		We propose a pipelined approach where alignment is followed by a classification step, in which we extract features representing high-level characteristics of the entailment problem, and pass the resulting feature vector to a statistical classifier trained on development data.
	www-nlp.stanford.edu /~wcmac/papers (1166 words)

	Construction of Meaning Workshop
		The PASCAL Recognizing Textual Entailment (RTE) Challenge is one attempt at a concrete formulation of the problem, containing examples such as
		I'll argue that, while graph-matching is the most promising of these avenues, it suffers from significant shortcomings, including flawed assumptions of locality and monotonicity.
		We use a pipelined approach where alignment is followed by a classification step, in which we extract features representing high-level characteristics of the entailment problem, and pass the resulting feature vector to a statistical classifier trained on development data.
	www-linguistics.stanford.edu /semgroup/semfest2006/maccartney.html (309 words)

	JOHAN50
		There is a simple NP which expresses the monotone decreasing quantifier -Q if and only if there is a simple NP with a weak non-cardinal determiner which expresses the monotone increasing quantifier Q. As Barwise and Cooper note,
		One way to test the negative character of the predicates in question is by verifying their monotonicity properties (cf.
		We might say that a predicate is negative just in case it reverses generalized entailment.
	odur.let.rug.nl /~hoeksema/docs/j50.htm (4073 words)

	Citebase - Probabilistic Default Reasoning with Conditional Constraints (Site not responding. Last check: 2007-10-22)
		In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints.
		We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts.
		Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:cs/0003023 (185 words)

	Generative Methodology thread
		At least two theoretical issues are involved here: the first is monotonicity vs non-monotonicity, and the second is the so-called "Closed World vs Open World Assumption".
		Now, suppose you want to model an exception, that is birds usually can fly but penguins cannot, and add statement "Penguins cannot fly": from this, you can infer that "Jack cannot fly".
		However, in a monotonic setting, statements that was previously "TRUE" remain "TRUE", so having both "Jack can fly" and "Jack cannot fly" assigned to "TRUE" yields to an inconsistency.
	www.bcngroup.org /beadgames/generativeMethodology/166.htm (2253 words)

	apex*
		One thing it clearly accomplishes is to show that monotonicity "goes with" -- is implicit in -- our (classical) concept of validity, as opposed to, say, the various alternative concepts discussed in the literature on nonmonotonic logic.
		A prominent example is the so-called "first-orderization" of entailment relations already discussed.
		As we have seen, platonic objects can also turn up in contexts where they are representationally essential: contexts where they faciliate the expression of contents that are not the literal contents of any English sentence.
	www.mit.edu /~yablo/apex.html (15021 words)

	[No title]
		If we ignore the presupposition, the entailment in (1) appears to be valid.
		This is a pragmatically induced type of downward entailment: (16) I am glad we got tickets.
		And of course much of everyday reasoning with conditionals is perfectly monotonic.
	odur.let.rug.nl /~hoeksema/fintel.doc (1602 words)

	SICStus Prolog - Constraint Logic Programming over Finite Domains (Site not responding. Last check: 2007-10-22)
		The heart of the constraint solver is a scheduler for indexicals [Van Hentenryck et al.
		If a constraint is reified or occurs in a propositional formula, the definition must contain four clauses for solving and checking entailment of the constraint and its negation.
		becomes monotone before admitting the propagating indexical for execution.
	www.cl.cam.ac.uk /ailanguages/sicstus3.7/sicstus_33.html (6441 words)

	THE NEED FOR NONMONOTONIC REASONING (Site not responding. Last check: 2007-10-22)
		This is because the well known systems of mathematical logic have the following monotonicity property.
		Since adding more sentences to A might make P applicable to more tuples, circumscription is not monotonic.
		Conclusions derived from circumscription are conjectures that A includes all the relevant facts and that the objects whose existence follows from A are all the relevant objects.
	www-formal.stanford.edu /jmc/circumscription/node2.html (451 words)

	Default reasoning from conditional knowledge bases: Complexity and . . . - Eiter, Lukasiewicz (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		A number of entailment semantics for conditional knowledge bases have been proposed in the literature.
		However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their...
		57 Conditional entailment: Bridging two approaches to default r..
	sherry.ifi.unizh.ch /374118.html (1365 words)

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