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Topic: Logical implication

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Entailment - Wikipedia, the free encyclopedia Implication or entailment is used in propositional logic and predicate logic to describe a relationship between two sentences or sets of sentences. Definition: A logically entails B if, by assuming all sentences in A and applying a finite sequence of inference rules to them (for example, those from propositional calculus), one can derive all sentences in B. This is, of course, relative to a specific logic (proof calculus). en.wikipedia.org /wiki/Entailment   (380 words)

Mathematical logic - Wikipedia, the free encyclopedia Attempts to treat the operations of formal logic in a symbolic or algebraic way were made by some of the more philosophical mathematicians, such as Leibniz and Lambert; but their labors remained little known and isolated. Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. Earlier appellations were symbolic logic (as opposed to philosophical logic); and metamathematics, which is now restricted as a term to some aspects of proof theory. en.wikipedia.org /wiki/Symbolic_logic   (982 words)

Chapter IV Logical implication in this sense is frequently distinguished from material implication, in that the former holds for a meaning relation dependent in part upon the factual status of the sentences related, whereas the latter holds for a truth-functional relation not dependent upon the factual status of the sentences related. The "paradox of material implication" is dispelled by the clear understanding that the " if-then " (that is, the " É ") relation, as some logicians use it, is not intended to restrict what can be meant but solely to restrict truth-functional relations among whatever is meant by the data related. In sum, logical argument consists of logical form or logical formulation of relations among variables; such logical form is symbolized by means of conventional notation. www.sjsu.edu /logic/symbolic.htm   (5384 words)

Body The construction of standard logics to fit the requirements of relatively well developed systems of scientific thought and inference is mirrored in the basic binary form of logical operations. Logical linkages are rendered with a view to logical priority, and rarely position in time. Standard theories of logic aim at the systemization of logical operations that are recognized in science and mathematics. www.psychodiagnostics.com /Cog_nbo.htm   (3157 words)

The Review of Metaphysics: Logical implication and the ambiguity of extensional logic.@ HighBeam Research Logical implication and the ambiguity of extensional logic. Extensional logic is profoundly ambiguous in that expressions using logical operators such as the conditional or conjunction are given two different senses. Modern logical systems based on the 'Principia Mathematica' which are commonly termed 'extensional logic' are actually pervaded by intensional logic. www.highbeam.com /library/doc0.asp?DOCID=1G1:14731588&refid=ip_encyclopedia_hf   (206 words)

logical implication - a Whatis.com definition Logical implication is a type of relationship between two statements or sentences. As an example of logical implication, suppose the sentences A and B are assigned as follows: However, the sense of logical implication is reversed if both statements are negated. whatis.techtarget.com /definition/0,,sid9_gci833443,00.html   (190 words)

The "logic" Of Logical Positivism - Objectivism Online Forum Logical implication is fine when used in the correct context, the problems only arise when people start thinking it has anything in common with the 'if' statement in natural language (ie when the concept "goes on holiday", to borrow an expression from Wittgenstein). Logical positivism states that the meaning of an empirical proposition is the means of its verification. Logical Postivism has trouble giving an account of how a theory is to be constructed, as the construction of theories would seem to be a rather rationalist enterprise. forum.objectivismonline.net /index.php?showtopic=3198   (2197 words)

Citations: A non-classical logic for information retrieval - van Rijsbergen (ResearchIndex) The basis of a logical model for IR is the assumption that queries and documents can be represented by logical formulas and that the matching process is founded on the notion of logical inference. Given d, a logical representation of a document, and q, a logical representation of a query, retrieval is simply establishing whether d j= q. The earliest approaches were directed at the use of classical logics, like Boolean logic [4] The basis of a logical model for IR originates in the work of Cooper who introduced an objective notion of relevance termed logical relevance [5] Cooper provides a formal definition of relevance in.... citeseer.ist.psu.edu /context/166206/0   (3154 words)

The Meanings of Logical Constants Furthermore, the roles logical constants play in reasoning are determined by the logical implications that depend on those logical constants, where these implications are determined by the contribution logical constants make to truth conditions. Since these results are logically equivalent, the two connectives make exactly the same contributions to truth conditions and are subject to exactly the same rules of logical implication, even though they do not have the same meaning. The other is that the meaning of a logical constant is determined by certain principles of logical implication involving that constant. www.nyu.edu /gsas/dept/philo/courses/concepts/meaning.html   (3173 words)

Philosophy 4 Introduction to Logic When we study logic, then, we are mainly trying to define, extend and apply the idea of logical implication. In applied logic we are very interested in questions of implication, but we also take into account the fact that people assert logical relationships for very different purposes. Deductive implication is the central concept in pure logic, but there are many cases in which P deductively implies C which strike most people as peculiar. www.csus.edu /indiv/m/mayesgr/phl4intro.htm   (1984 words)

IntroApplTEST4notesSUM04.doc --be able to write the converse of an implication --be able to write the contrapositive of an implication --know and recognize biconditionals (‘if and only if”)(symbol: () --know the order for logical connectors: 1. homepages.dsu.edu /shiersa/documents/IntroApplTEST4notesSUM04.doc   (34 words)

Peter Suber, "Glossary of First-Order Logic" A property possessed by all the wffs in a set is logically hereditary iff the accepted rules of inference pass it on (transmit it) to all the conclusions derivable from that set by those rules. Two consequences of the formal definition of material implication that violate informal intuitions about implication: (1) that a material implication is true whenever its antecedent is false, and (2) that a material implication is true whenever its consequent is true. A wff A of propositional logic created from a wff B of predicate logic by (1) removing the quantifiers from B, and (2) replacing each predicate symbol (and its arguments) in B with a propositional symbol. www.earlham.edu /~peters/courses/logsys/glossary.htm   (9715 words)

Math Notes - Relations Theorem 5 connects the relation concept of implication to the subset concept of implication. The derivation uses the identity relation in the relation model of the implication. Logical constant true corresponds to the universal set of discourse U. home.att.net /~p.konieczko/mathrel13.html   (1153 words)

5 Testing for a tautology, testing two propositions for equivalence, testing for logical implication, and so forth, can all be done by construction and comparing truth tables. The logical connectives obey logical-equivalence-preserving algebraic laws, analgous to the laws of arithmetic. Logical equivalence and the substitution theorems were reviewed. www.cs.indiana.edu /classes/s251/lec/5   (626 words)

The Atheism Web: Logic & Fallacies The symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. It was also believed at one time that Euclidean geometry was a universal law; it is, after all, logically consistent. Logic in itself doesn't solve the problem of verifying the basic assertions which support arguments; for that, we need some other tool. www.infidels.org /news/atheism/logic.html   (5794 words)

ae.htm This is true whether the implication in question be causal, or logical in that narrower sense to which it has been professionally restricted and to which, for present purposes, I shall also restrict it. Nagel to the contrary, I believe that this is a respectable position provided that logical implication or entailment is not identified with the 'subject-matter neutral' implication which, until recently, has been the primary object of attention by professional logicians. Thus to characterize a person's utterances by quoting sentences containing logical words is to imply that the corresponding sounds function properly in the verbal behavior in question and to imply that the uniformities characteristic of these ways of functioning are present in his sayings and proximate dispositions to say. www.ditext.com /sellars/ae.html   (6431 words)

Logical_implication.doc Certain properties about implication can be deduced or negated for example: ((p(q) (((p ((q) If p(q is true in a world does not entail that p is true in a world and that q is true in a world. for modal propsitional logic consists of: a non-empty set W of possible worlds a binary relation of accessibility R between possible worlds in W. a valuation V that gives, in every possible world, a value Vw(p) to each proposition letter p. In a world w a triple t is true when it is true in w or any other world w’ taking into account the trust factor. www.agfa.com /w3c/2002/02/thesis/Logical_implication.doc   (1657 words)

Untitled Logical Implication Principle The fact that one's view logically implies P can be a reason to accept P. Logical Inconsistency Principle Logical inconsistency is to be avoided. Logical Closure Principle One's beliefs should be "closed under logical implication." In other words there is something wrong with one's beliefs if there is a proposition logically implied by them which one does not already believe. Again, consider defense of a "logic of entailment," which observes (1) in standard logic a contradiction logically implies any proposition at all, and (2) one is not justified in responding to the discovery that one's view is inconsistent by inferring anything whatsoever, concluding that (3) a new logic is needed (Meyer 1971). www.cs.umu.se /kurser/TDBC12/HT99/harman.html   (6807 words)

ipedia.com: Theory Article In mathematics, a theory is a set of statements closed under logical implication. In mathematical logic, "theory" is the term for a set of well-formed formulae consisting of certain axioms and all theorems provable from said axioms. A theory is also different from a physical law in that the former is a model of reality whereas the latter is a statement of what has been observed. www.ipedia.com /theory.html   (1254 words)

Logic: Clarification of Terms and Concepts in Sentence Logic   Thus, any valid argument that is represented by conjoining the premises to imply the conclusion will be a logical implication since its truth table analysis will yield a tautology and all tautologous statements whose major connective is an implication are logical implications. Logic: Clarification of Terms and Concepts in Sentence Logic Tautology:  a compound sentence that is true regardless of the truth values of its component atomic sentences. pegasus.cc.ucf.edu /~stanlick/slterms.htm   (520 words)

gwd94.txt Thus, my project herein is to assail the empirical truth of the premises, not the logical truth of the argument itself, whereby I hope to block the application of the implication to the world understood empirically. Once the truth of the premises is questioned, the utility of the logical implication from them to the conclusions in establishing truth will also come under suspicion. However, this distinction in focus should not lead one to assume that I have accepted the logical merits of the argument. www.textfiles.com /magazines/GWD/gwd94.txt   (1233 words)

implication - OneLook Dictionary Search Phrases that include implication: logical implication, material implication, easement by implication, paradoxes of material implication, two-way implication, more... Words similar to implication: deduction, entailment, implicating, implicative, implicatively, implicativeness, import, significance, conditional relation, logical implication, more... noun: a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=implication   (362 words)

Echo BASIC - Logical operators Logical implication, by way of contrast, is not a statement connective at all. In formal logic, logical implication is often written using a double arrow (I'll type It invites confusion between two quite distinct notions: logical implication and (borrowing another _Principia_ usage) material implication. outer-court.com /basic/echo/T649.HTM   (477 words)

Models, Truth, Logical Implication, and Validity Logical implication is defined in Definition 1.9.1 on p. Finally, we turn to Leary's definitions of logical implication and validity. Notice that a structure models a formula if and only if the sentence that results from prefixing to the formula universal quantifiers binding all the free variables of the formula results in a sentence that is true in the structure. www.trinity.edu /cbrown/topics_in_logic/struct/node3.html   (474 words)

liuji114.txt It is well-known that the logical implication of conditional independence (CI) in probability theory and embedded multivalued dependency (EMVD) in relational database theory coincides for the class of BNs and for the class of MNs. It is also well-known that the logical implication of CI and EMVD differs in general. This intriguing result is important as it provides a lower upper-bound on where the logical implication of CI and EMVD diverge. www.cs.uregina.ca /~pwlfong/CS499/Abstracts/liuji114.txt   (189 words)

MaterialCon logical constant is inessential in that it, or the content it expresses, may be freely sub- logical consequence and the logical truth of a conditional, we have logical validity that rely on notions of substitutivity and logical form. sun.soci.niu.edu /~phildept/Kapitan/matcons.html   (8023 words)

2.5 Logical Intentionality The rules of LKA capture a concept of logical implication and subjunction that does not respect this differentiation. If implication is not taken to be a mere truth-functional term, but is conceived in terms of inference, then in some sense none of the sequents (1) to (4) represents a valid rule of inference. Its concept is a logical account of the order Husserl has described in terms of intentionality. www.hf.uio.no /filosofi/njpl/vol4no1/connexive/node10.html   (942 words)

Nalanda Digital Library - Roget's Thesaurus of Synonyms & Antonyms - 526. Latency. Implication. indirect, crooked, inferential; by inference, by implication; implicit; constructive; allusive, covert, muffled; steganographic[obs3]; understood, underhand, underground; delitescent[obs3], concealed &c. www.nalanda.nitc.ac.in /reference/general/Roget/matter550.html   (165 words)

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