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Topic: Logical equivalence

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	Logical equivalence - Wikipedia, the free encyclopedia
		In logic, statements p and q are logically equivalent if they have the same logical content.
		Logical equivalence is often confused with material equivalence.
		The logical equivalence of p and q is sometimes expressed as p ≡ q or p ⇔ q.
	en.wikipedia.org /wiki/Logical_equivalence (289 words)

	ipedia.com: Logical conjunction Article (Site not responding. Last check: 2007-11-06)
		In logic and technical fields that use it, conjunction, or and, is a logical operator in logical calculi, and a rule of inference in deductive systems.
		Logically, the sentence "it's raining, but the sun is shining" is equivalent to "it's raining, and the sun is shining", so logically, "but" is equivalent to "and".
		On the other hand, in Brazilian logic, the logical equivalence is broken between A BUT NOT B (where "BUT NOT" is a single operator) and A AND (NOT B), which is a weaker statement.
	www.ipedia.com /logical_conjunction.html (552 words)

	Section 1.1 Review
		To test for logical equivalence of 2 statements, construct a truth table that includes every variable to be evaluated, and then check to see if the resulting truth values of the 2 statements are equivalent.
		The negation of a conjunction (logical AND) of 2 statements is logically equivalent to the disjunction (logical OR) of each statement's negation.
		Logical equivalencies can be used to simplify statement forms, to confirm or disprove an equivalency, to create efficient and logically correct computer programs, or to aid in the design of digital logic circuits.
	www.keyano.ca:8080 /mejsmont/courses/bus112/DM/chapters/review1_1.html (757 words)

	Logical biconditional - Wikipedia, the free encyclopedia
		In logical calculus of mathematics, logical biconditional (sometimes also known as the material biconditional) is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent).
		The antecedent is the subject and the consequent is the predicate of a universal affirmative proposition.
		means that a implies b and b implies a; in other words, that the propositions are equivalent, that is to say, either true or false at the same time.
	en.wikipedia.org /wiki/Logical_biconditional (586 words)

	Philosophy 160 (002): Formal Logic
		Logic, as a subject, is concerned with a family of related notions.
		Logical truth, logical falsity and logical indeterminacy; logical consistency and logical equivalence; deductive validity.
		Note that deductive validity is a property of arguments; logical truth, falsity, and indeterminacy are properties of sentences; and logical consistency and equivalence are properties of pairs or sets of sentences.
	www.umsl.edu /~phiablac/philosophy160/Lesson1.htm (1491 words)

	Logical equivalence between generalized urn models and finite automata
		The logical equivalence of automaton models (AM) with generalized urn models suggests that these logics are more general and ``robust'' with respect to changes of the particular model than could have been expected from the particular instances of their first appearance.
		Another equivalence scheme uses the fact that both automaton partition logics and the logic of generalized urn models have a separating (indeed, full) set of dispersion-free states.
		We have explicitly demonstrated the logical equivalence of generalized urn models and and the logic of finite automata, both by a direct construction and by an indirect construction utilizing the set of two-valued states.
	tph.tuwien.ac.at /~svozil/publ/2001-eua.htm (2305 words)

	Logical equivalence problem
		Therefore, it is not to be expected that it is possible to devise a serious logic for natural language semantics, in which logical equivalence is decidable.
		Even though the problem of logical equivalence in general is undecidable, it may be the case that we can devise techniques which solve at least part of the problem; i.e.
		The point then is, that even though we have not much to say about the logical equivalence problem, we argue that the results of this thesis are not dependent on the way in which this problem is solved eventually.
	odur.let.rug.nl /~vannoord/papers/diss/diss/node8.html (985 words)

	A Note On Mr. De Morgan
		The De Morgan logical equivalence denying the dot, ^(p.q), is demonstrated by the identity of the truth tables in column 6 and column 9.
		The De Morgan logical equivalence denying the wedge, ^(p v q), is likewise demonstrated by the identity of the truth tables in columns 8 and 10.
		The definition of a logical equivalence as a tautologous material equivalence is an alternative to defining two propositions to be logically equivalent when they have identical truth tables.
	www.apa.udel.edu /apa/archive/newsletters/v96n2/teaching/morgan.asp (1593 words)

	OpenVMS User's Manual
		By default, the DEFINE command places logical names in your process logical name table (see Section 11.8), where the logical name is available only to your process and subprocesses.
		If a logical name is to be used by a privileged image, including a utility, it must be defined in executive or kernel mode in an executive or kernel mode table.
		After the system translates a logical node name at the local node, it parses the rest of the file specification to determine whether the format is valid.
	www.uni.edu /connelly/vmsos731/vmsos731/6489/6489pro_026.html (2749 words)

	Maggie Johnson
		Logical Consequence: A sentence S is a logical consequence of a set of premises if it is impossible for the premises all to be true while the conclusion is false.
		Logical Possibility: A sentence or claim is logically possible if there is a possible circumstance in which it is true.
		Logically equivalent sentences can be substituted for one another in the context of a larger sentence and the resulting sentences will also be logically equivalent.
	cse.stanford.edu /classes/cs103a/h7Consequence.html (667 words)

	[No title]
		Logical equivalence and the substitution theorems were reviewed.
		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.
	www.cs.indiana.edu /classes/s251/lec/5 (626 words)

	logical equivalence - a Whatis.com definition (Site not responding. Last check: 2007-11-06)
		Logical equivalence is a type of relationship between two statements or sentences in propositional logic or Boolean algebra.
		B) Logical equivalence is important in the design of digital circuits.
		Several circuits may be logically equivalent, in that they all have identical truth tables.
	searchsmb.techtarget.com /gDefinition/0,,sid44_gci833433,00.html (188 words)

	T3.4 p.1 Logical Equivalence in SL
		The two members of a pair of sentences are logically equivalent if and only if it is not possible for one of the pair to be true while the other is false.
		Notice that this definition of logical equivalence in SL is just like the general definition of logical equivalence except that in SL we can say exactly what is possible in terms of truth value assignments.
		To test for the logical equivalence in SL, one simply constructs ONE truth table for whatever pair of sentences is in question and checks to see that there is no row making one sentence true and the other false.
	www.oakland.edu /phil/cafe/Tch3_4Equiv1.htm (564 words)

	Russell-Myhill Paradox [Internet Encyclopedia of Philosophy]
		However, it appears that if Frege's logical systems were expanded to include commitment to the realm of sense, to make it possible to refer not only to truth-values and classes, but thoughts and other senses, a version of the antinomy would be provable.
		The commitment to logical entities in a Platonic realm has grown less and less popular, especially given the widespread view that logic ought to be without ontological commitment.
		One might, for example, adopt logical equivalence as being a sufficient condition for propositions to be identical.
	www.iep.utm.edu /p/par-rusm.htm (3073 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Defines the equivalence name, usually a file specification, device name, or other logical name, to be associated with the logical name in the specified logical name table.
		The mode of the logical name must be the same as or external to (less privileged than) the mode of the table in which you are placing the name.
		Note that the logical name TEMP was terminated with a colon in the ASSIGN command, but that the command interpreter deleted the colon before placing the name in the logical name table.
	pharmchem.kfunigraz.ac.at /help?key=ASSIGN&extract=yes (2143 words)

	Truth Conditions and Subject Matter (Site not responding. Last check: 2007-11-06)
		All logical truths are logically equivalent; if we take logical equivalence as a criterion for sameness of truth conditions, they will all designate the same thing according to (A).
		Barwise and I criticized logical equivalence as a criterion of sameness of designation, on the basis of considerations like those adumbrated in the last few paragraphs, and on this basis, rejected redistribution steps.
		The argument Gödel uses does not rely on the logical equivalence criterion, but on a specific and intuitively plausible claim that two sentences have the same content.
	www-csli.stanford.edu /~john/evading/evading/node5.html (677 words)

	OpenVMS Cluster Systems (Site not responding. Last check: 2007-11-06)
		If you attempt to create a new clusterwide logical name with the same access mode and identical equivalence names and attributes as an existing clusterwide logical name, the existing name is not deleted, and no messages are sent to remote nodes.
		In contrast, when one process modifies the clusterwide logical name database, the change is visible immediately on that node, but it takes a short time for the change to be propagated to other nodes.
		Until a booting node's copy of the clusterwide logical name database is consistent with the logical name databases of the rest of the cluster, any attempt on the booting node to create or delete clusterwide names or tables is stalled transparently.
	www.cuis.edu /doc_vms_html/000000/731final/4477/4477pro_007.html (2888 words)

	OpenVMS User's Manual (Site not responding. Last check: 2007-11-06)
		The system stores logical names and their equivalence strings in process, job, group or system logical name tables.
		Logical names that identify logical name tables or that translate iteratively to logical name tables must always be entered into one of the directory logical name tables.
		Before a logical name is created, the size of its data structure is checked against the quota remaining for the table.
	pupgg.princeton.edu /cdrom12/html/ssb71/6489/6489P021.HTM (3518 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		[Copi/Cohen, 385] Logical Equivalence is important because two propositions which are logically equivalent MEAN the same thing, even though they might be written up differently in English.
		It is also evident that Logical Equivalence is defined, in part, by Material Equivalence since Logical Equivalence includes a biconditional.
		The conditional statement merely connects the elements of the argument using the symbols for "and" (between each premise) and "if...then" (for the argument as a whole), with the appropriate grouping by brackets.
	condor.depaul.edu /~mlarrabe/logic/wk8b.htm (338 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		You can create a logical name in the same mode as the table in which you are placing the name, or in an outer mode.
		The mode of the logical name must be the same as or less privileged than the mode of the table in which you are placing the name.
		User-mode logical names created within the process logical name tables are used for the execution of a single image; for example, you can create a user-mode logical name to allow an image executing in a command procedure to redefine SYS$INPUT.
	pharmchem.kfunigraz.ac.at /help?key=DEFINE&extract=yes (4398 words)

	Logical Equivalence
		To test whether or not two propositions are logically equivalent we make a truth table for each of them and compare their last columns.
		It is logically equivalent to its contrapositive, "If I am not taller than you then you are not under five feet tall".
		Also its converse, "If I am taller than you then you are under five feet tall", is logically equivalent to its inverse, "If you are not under five feet tall then I am not taller than you".
	sinnamon.math.uwo.ca /courses/031/LogicEquivalence.htm (348 words)

	No Title
		If two formulas are logically equivalent, their syntax may be different, but their semantics is the same.
		These equivalences can be used to transform a formula into a logically equivalent one of a certain syntactic form (called a ``normal form'').
		Note that implication is logically equivalent to the contrapositive, and that the inverse is logically equivalent to the converse!
	www.cs.sunysb.edu /~skiena/113/lectures/lecture3/lecture3.html (662 words)

	Universal Algebra and Logic Seminars
		Title: Equivalence of logical consequence operations: an order theoretic perspective, V. Abstract: The aim of this series of talks is to propose and study an order theoretic and categorical framework for the study of the general notion of an abstract logical equivalence between two logical consequence relations.
		Title: Equivalence of logical consequence operations: an order theoretic perspective, I. Abstract: The aim of this series of talks is to propose and study an order theoretic and categorical framework for the study of the general notion of an abstract logical equivalence between two logical consequence relations.
		We show that these systems are equivalent and that they constitute equivalent algebraic semantics for the class of non-associative residuated lattices.
	sitemason.vanderbilt.edu /page/f0Cdhu (2086 words)

	Logical equivalence
		It is easy to use thruth tables to find out if two given expressions are logically equivalent.
		If they are identical then they are logically equivalent other wise not.
		Such simplifications are used in constructing logically efficient computer programs and in designing digital logic circuits.
	www.infocom.cqu.edu.au /Courses/aut2001/84100/Study_Material/WEEK4/node3.html (443 words)

	Statement Forms
		Statements that are substitution-instances of these two component statement-forms are then said to be logically equivalent: no matter what their content may happen to be, the conditions for their truth or falsity are exactly the same.
		Again, the logical equivalence of these three expressions provides us with a convenient way to comprehend and employ what is asserted in any statement of material equivalence.
		The truth-table at the right shows that these statement forms are not logically equivalent, since the biconditional connecting them is contingent.
	www.philosophypages.com /lg/e10c.htm (708 words)

	[No title]
		We define logical equivalence and prove that (1) declarative equivalence implies logical equivalence, and that (2) logical equivalence implies algorithmic equivalence.
		As lemmas we also show that logical equivalence is an equivalence relation and that weak-head reduction is sound.
		\end{itemize} We conjecture that the logical equivalence is not essential for the completeness proof: we could strengthen the completeness lemma such that the logical property of the function type is satisfied (which is the same as proving algorithmic-logical soundness), and then prove the strengthened completeness lemma directly (which is the same as proving declarative-logical completeness).
	www.cis.upenn.edu /~stse/equiv/main.tin (1767 words)

	Philosophy 2700: Mathematical Logic (Site not responding. Last check: 2007-11-06)
		Note that deductive validity and soundness are properties of arguments; logical truth, falsity, and indeterminacy are properties of sentences; and logical equivalence is a property of pairs of sentences.
		The logical form of a sentence is writ-ten out with the aid of symbols.
		In this section, Sentential Logic (SL), we uncover certain preliminary aspects of logical form; in Predicate Logic, which is covered in Section II of the course, we uncover some further aspects of logical form.
	cdis.missouri.edu /previews/2160/lesson01.htm (1440 words)

	Utterances and meaning
		On the other hand, there is much less agreement as to what the `meaning' of natural language utterances is, and how that meaning should be represented.
		In a model theoretic view on meaning, the meaning of utterances is represented by logical formulas.
		However, what kind of logic is needed to describe meanings of natural language is a matter of debate.
	odur.let.rug.nl /vannoord/papers/diss/diss/node7.html (307 words)

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