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Topic: Deduction theorem

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	Deduction theorem -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-29)
		In mathematical (The branch of philosophy that analyzes inference) logic, the deduction theorem states that if a formula F is deducible from E then the implication E → F is demonstrable (i.e.
		The deduction theorem may be generalized to a countable sequence of assumption formulas such that from
		The deduction theorem is a meta-theorem: it is used to deduce proofs in a given theory though it is not a theorem of the theory itself.
	www.absoluteastronomy.com /encyclopedia/D/De/Deduction_theorem.htm (113 words)

	The Graphical Logic of C. S. Peirce - Appendix
		But a statement of the deduction theorem for these systems is itself, I think, of considerable general interest.
		Actually, there is no trick to merely stating the deduction theorem for any system.
		But by the deduction theorem for these systems, the schema we wished to prove is proven.
	www.clas.ufl.edu /users/jzeman/graphicallogic/appendix.htm (963 words)

	How definitive is the standard interpretation of Gödel's Incompleteness Theorem?
		We show that such interpretations are inconsistent with a standard Deduction Theorem of first order theories.
		It follows that the standard interpretations of Gödel’s reasoning are inconsistent with a standard Deduction Theorem of an arbitrary first order theory ([Me64], p61, Corollary 2.6).
		Theorem 2 as a valid inference, such interpretations are inconsistent with the standard Deduction Theorem for an arbitrary first order theory
	alixcomsi.com /How_definitive_is_the_standard.htm (2027 words)

	Quotation
		The aim of this paper is to sketch a theory of abduction with its relations with deduction and induction in the sense of the second Peirce.
		In the syllogistic approach, exemplified by the celebrated Barbara syllogism, deduction is the type of reasoning which allows deriving, from a major premiss (the rule) and a minor premiss (the case), a conclusion (the result).
		This representation theorem is given in two forms : theorem 1 links abduction and deduction ; theorem 1’ prepares the link between abduction and induction, through the belief revision operator.
	www.marilia.unesp.br /atividades/extensao/revista/v2/artigo1.html (6185 words)

	Chapter 12: The Systems of Complete Modalization - Alternative Formulations
		We may note that in Zeman 1967b deduction from hypotheses is defined in a manner differing slightly from that of the present section.
		Although the deduction theorem can be proved with this stronger definition of deduction, the converse of the deduction theorem cannot, and so the present notion of deduction is preferable.
		There is, indeed, a sense in which the deduction theorem does hold in T and S2, but I feel that it is a fairly trivial sense.
	www.clas.ufl.edu /users/jzeman/modallogic/chapter12.htm (3723 words)

	Intuitionistic Logic
		A derivation of a formula E from a collection F of assumptions is any sequence of formulas, each of which belongs to F or is an axiom or an immediate consequence, by a rule of inference, of preceding formulas of the sequence, such that E is the last formula of the sequence.
		To illustrate the usefulness of the Deduction Theorem, consider the (apparently trivial) theorem schema (A → A) of IPC.
		The Deduction Theorem tells us there is a proof P in IQC of (A(x) → ¬∀x¬A(x)), and one application of ∃-introduction converts P into a proof of ∃x A(x) → ¬∀x¬A(x).
	plato.stanford.edu /entries/logic-intuitionistic (6042 words)

	Fregean Logics With The Multiterm Deduction Theorem And Their Algebraization - Czelakowski, Pigozzi (ResearchIndex) (Site not responding. Last check: 2007-10-29)
		A deductive system S (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas f hff; fii : T; ff `S fi and T; fi `S ff g; is a congruence relation on the formula algebra.
		The multiterm deduction-detachment theorem is a natural generalization of the deductive theorem of the classical and intuitionistic propositional calculi (IPC) in which a finite system of possibly compound formulas collectively...
		...of Corollary 5.7 because by [13, Theorem 2] a Fregean protoalgebraic logic with theorems is regularly finitely algebraizable.
	citeseer.ist.psu.edu /czelakowski98fregean.html (591 words)

	Methods of mathematics proof
		Deduction Theorem justifies the technique known as the Rule of Conditional Proof (CP).
		Z) So you see, a proof of a theorem in a branch of mathematics uses the rules, definitions, axioms, and theorems of that branch of mathematics along with the rules of Logic.
		We recommend that a Proof by Contradiction be one that begins with p and ~q and ends up obtaining the negation of the premise, and that a Reductio Ad Absurdum Proof be one that ends up obtaining any contradiction of a known truth.
	www.mathpath.org /proof/proof.methods.htm (2455 words)

	Deduction theorem - Encyclopedia, History, Geography and Biography
		Deduction theorem - Encyclopedia, History, Geography and Biography
		In mathematical logic, the deduction theorem states that if a formula F is deducible from E then the implication E → F is demonstrable (i.e.
		This encyclopedia, history, geography and biography article about Deduction theorem contains research on
	www.arikah.net /encyclopedia/Deduction_theorem (173 words)

	Fully Adequate Gentzen Systems And The Deduction Theorem - Font, Jansana, Pigozzi (ResearchIndex)
		It is proved in [13] that, in the presence of the uniterm deduction detachment theorem, the Fregean principle essentially...
		Fregean Logics With The Multiterm Deduction Theorem And..
		5 Abstract algebraic logic and the deduction theorem (context) - Blok, Pigozzi
	citeseer.ist.psu.edu /412026.html (621 words)

	Review Natural deduction theorem proving via higher-order resolution (Technical report. University of Cambridge. ... (Site not responding. Last check: 2007-10-29)
		Review Natural deduction theorem proving via higher-order resolution (Technical report.
		Book / Natural deduction theorem proving via higher-order resolution (Technical report.
		Natural deduction theorem proving via higher-order resolution (Technical report.
	computertoaster.com /reviews/asinsearch_B0007BYOSQ (48 words)

	New forms of the Deduction Theorem and Modus Ponens (Site not responding. Last check: 2007-10-29)
		This paper studies, with techniques of Abstract Algebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule.
		In passing we have found new, alternative presentations of positive implicative logic, both in Hilbert style and in Gentzen style, and have characterized it in terms of the restricted Deduction Theorem: it is the weakest logic satisfying Modus Ponens and the Deduction Theorem restricted to at most 2 side formulas.
		The algebraic part of the work has lead to the class of quasi-Hilbert algebras, a quasi-variety of implicative algebras introduced by Pla and Verdin 1980, which is larger than the variety of Hilbert algebras.
	cms.jcmf.cz /czech-catalan/Font (247 words)

	deduction theorem - OneLook Dictionary Search (Site not responding. Last check: 2007-10-29)
		Tip: Click on the first link on a line below to go directly to a page where "deduction theorem" is defined.
		Deduction Theorem : Eric Weisstein's World of Mathematics [home, info]
		deduction theorem : FOLDOP - Free On Line Dictionary Of Philosophy [home, info]
	onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=deduction+theorem (94 words)

	Propositional Logic
		These natural deduction systems present the logic by describing introduction and elimination rules for the connectives.
		All of the natural deduction rules can be derived, though we only sketch a few of these rules.
		The sequence demonstrates this fact because: (a) it is finite in length, (b) lines 1, 2, and 3 are all premises, and (c) lines 4 and 5 follow from previous lines by Modus Ponens.
	mally.stanford.edu /tutorial/sentential.html (1059 words)

	Automated Reasoning
		A special-purpose theorem prover does not draw its main benefit by restricting its attention to the domain axioms but from the fact that the domain may enjoy particular theorem-proving techniques which can be hardwired — coded — within the reasoning program itself and which may result in a more efficient logic implementation.
		Implementations of automated theorem proving systems using NK deduction have been motivated by the desire to have the program reason with precisely the same proof format and methods employed by the human user.
		Their theorem prover is written in the functional programming language Lisp which is also the language in which theorems are represented.
	plato.stanford.edu /entries/reasoning-automated (12208 words)

	An arguable addition to the standard Deduction Theorems of first order theories
		We consider an arguable addition to the standard Deduction Theorems of first order theories.
		We have argued that Meta-theorem 2 is a valid Deduction Theorem of any first order theory.
		We note that Gödel’s Incompleteness Theorems assume significance only if we presume that the arithmetic, in which they are derived, can be omega-consistent (cf.
	alixcomsi.com /An_arguable_addition.htm (2153 words)

	Dr Don Pigozzi (Site not responding. Last check: 2007-10-29)
		Revised notes of lectures on joint work with Katarzyna Palasinska given at the CAUL, Lisbon in September of 2003, and at the Universidad Catolica, Santiago in November of 2003.
		Abstract algebraic logic and the deduction theorem (draft).
		Fregean logics with the multiterm deduction theorem and their algebraization.
	orion.math.iastate.edu /dpigozzi (127 words)

	Can the deduction theorem be used recursively? (Site not responding. Last check: 2007-10-29)
		Uh, the deduction theorem isn't a rule of inference in the sense that
		theorem can often be used as a rule.
		deduction theorem says that there is a deduction of S - A -> B if and
	www.groupsrv.com /science/about38068.html (2201 words)

	[4-18] Automated Deduction/Theorem Proving (Site not responding. Last check: 2007-10-29)
		[Contains Prolog code for a simple resolution-based theorem prover.] C. Chang and R.C. Lee, "Symbolic Logic and Mechanical Theorem Proving", Academic Press, 1973.
		David Duffy, "Principles of Automated Theorem Proving", John Wiley and Sons, 1991.
		Proceedings of the 11th International Conference on Automated Deduction (CADE-11), D. Kapur (editor), Saratoga Springs, NY, USA, June 15-18, 1992, Lecture Notes in AI 607, Springer-Verlag, 1992, 793 pages.
	www.faqs.org /faqs/ai-faq/general/part4/section-19.html (178 words)

	Propositional Logic. Mathematical Logic. Part 2.
		Hence, by Deduction Theorem 1, A - B->BandA.
		Hence, by Deduction Theorem 1, A - BandA->B. Exercise 2.2.3.
		This theorem provides a kind of a "constructive embedding" for the classical propositional logic: any classically provable formula can be "proved" in the constructive logic, if you put two negations before it.
	www.ltn.lv /~podnieks/mlog/ml2.htm (4435 words)

	ORA Canada Bibliography of Automated Deduction: S-T (Site not responding. Last check: 2007-10-29)
		[Slagle 1970a] J.R. Slagle, Interpolation theorem for resolution in lower predicate calculus, JACM 17(3):535-542, 1970.
		(A survey of four theorem provers), RSRE Memo 4430, Royal Signals and Radar Establishment, October 1990.
		[Tuominen 1990] H. Tuominen, Dynamic logic as a uniform framework for theorem* proving in intensional logic, Proc.
	www.ora.on.ca /biblio/biblio-prover-s-t.html (7376 words)

	School in Deduction and Theorem Proving
		To register, send name, affiliation, address, e-mail, dates of arrival/departure and a cheque in UK £ drawn on a UK bank to cover the registration fee and the number of nights of accommodation required.
		The cheque should be made payable to Heriot-Watt University and labelled "School in Deduction and Theorem Proving".
		In order to guarantee accommodation, it is advisable that your application is sent as soon as possible.
	www.cee.hw.ac.uk /~fairouz/ukiischool2000/ukiischool.html (589 words)

	Formal Methods Virtual Library (Site not responding. Last check: 2007-10-29)
		Boyer-Moore theorem prover (a forerunner of Nqthm and
		Isabelle, a generic theorem prover, supporting higher-order logic, ZF set theory, etc.
		TPS and ETPS, the Theorem Proving System and the Educational Theorem Proving System.
	www.afm.sbu.ac.uk (1633 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Yahya, Adnan, and Henschen, Lawrence J. Deduction in Non-Horn Databases, Vol.
		PARTHENON: A Parallel Theorem Prover for Non-Horn Clauses, Vol.
		Interaction with the Boyer-Moore Theorem Prover: A Tutorial Study Using the Arithmetic-Geometric Mean Theorem, Vol.
	www-unix.mcs.anl.gov /JAR/jar-keywords.html (8795 words)

	Foundations of Mathematics
		Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries - by Marvin J. Greenberg
		From Natural Deduction to Sequent Calculus - Slides by Christoph Benzmüller
		Metamath is a language for expressing theorems and their proofs
	sakharov.net /foundation_rt.html (2708 words)

	ORA Canada Bibliography of Automated Deduction: M-N (Site not responding. Last check: 2007-10-29)
		[McCune 1981] W.W. McCune, An inference mechanism for resolution-style theorem provers, M.A. thesis, Northwestern Univ., 1981.
		[Meltzer 1969] B. Meltzer, The use of symbolic logic in proving mathematical theorems by means of a digital computer, Foundations of Maths.
		[Montague 1956] R. Montague, L. Henkin, On the definition of formal deduction, The J. of Symbolic Logic 21, 1956.
	www.ora.on.ca /biblio/biblio-prover-m-n.html (7647 words)

	Grand Challenges for Automated Reasoning, Deduction, Theorem Proving and Model-Checking (Site not responding. Last check: 2007-10-29)
		Simon Colton's report of the panel on "Challenge problems for automated deduction (with special emphasis on mathematics)".
		The panel was held jointly by the RADM and PaPS workshops.
		Toby Walsh's position statement proposing a powerful mathematical assistant as a grand challenge for research in AI to this UK Computing Research Committee sponsored workshop.
	4c.ucc.ie /~tw/ar/gc.html (92 words)

	Predicate Logic. Mathematical Logic. Part 3.
		We will prove also that the meaning of a formula does not depend on the names of bound variables used in it.
		Glivenko's Theorem (see Section 2.7) provides a simple "constructive embedding" for the classical propositional logic: any classically provable formula can be "proved" in the constructive logic, if you put two negations before it.
		This theorem does not hold for the predicate logic.
	www.ltn.lv /~podnieks/mlog/ml3.htm (3086 words)

	Conference on Automated Deduction (Site not responding. Last check: 2007-10-29)
		An implementation of a tableau theorem prover for modal logics
		Deductive Search for Errors in Free Data Type Specifications Using Model Generation
		Deductive vs. Model-Theoretic Approaches to Formal Verification (Abstract of Invited Talk)
	wotan.liu.edu /docis/dbl/cadeca (2745 words)

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