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Topic: Inference rules

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	Rule of inference - Wikipedia, the free encyclopedia
		Prominent examples of rules of inference in propositional logic are the rules of modus ponens and modus tollens.
		Rules of inference must be distinguished from axioms of a theory, which are assertions that are assumed to be true without proof.
		Rules of inference play a vital role in the specification of logical calculi as they are considered in proof theory, such as the sequent calculus and natural deduction.
	en.wikipedia.org /wiki/Inference_rule (1066 words)

	Inference rule (Site not responding. Last check: 2007-11-06)
		In mathematical logic, an inference rule is a fundamental logical rule for carrying out deductions from a pair of premises to a conclusion.
		An inference rule operates on the axioms just as it operates on contingent hypotheses or on proven theorems: the rule does not distinguish between axioms, hypotheses, and theorems, but operates on them in the same fashion in order to obtain a conclusion.
		So inference rules are stronger than axioms, because axioms, though they may be solid and true, are nevertheless passive, whereas the inference rule is the action which joins statements together in order to create new statements.
	www.sciencedaily.com /encyclopedia/inference_rule (360 words)

	Propositional calculus - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-06)
		It is a set of axioms (which may be an empty set), and a set of inference rules for deriving new well-formed formulas (wffs) from a given set of wffs.
		Ideally the axioms and inference rules of a calculus are chosen such that if the formulas in a set are semantically true then any formulas derivable from them are also true.
		The last two rules however use hypothetical reasoning in the sense that in the premise of the rule we temporarily assume an (unproven) hypothesis to be part of the set of inferred formulas to see if we can infer a certain other formula.
	encyclopedia.worldsearch.com /propositional_calculus.htm (2923 words)

	Interrogating device for changing the priority of the inference rules - Patent 5027305
		Also, the backward inference rules are stored in the rule memory in the form which is added with a command for initiating a change of the priority added to the forward inference rules, a deletion of the rules and a restoration of the rules, should the necessity arise.
		Therefore the change of the priority for the foward inference rules, the deletion of the rule and the restoration of the rule may be easily accomplished by the action of the forward inference rule or the backward inference rule.
		Thus, in the forward inference control system, the change of the priority of the forward inference rule, the deletion of the rule and the restoration of the rule may be accomplished by the forward inference control unit.
	www.freepatentsonline.com /5027305.html (4907 words)

	Logical Consequence, Deductive-Theoretic Conceptions [Internet Encyclopedia of Philosophy]
		A proof of X from K that appeals exclusively to the inference rules of N is a formal deduction or formal proof.
		The defect of this rule, according to Anderson and Belnap is that "from" in "from the assumption of the antecedent P" is not taken seriously.
		Apart from the negation rules, it is fairly straightforward to dress the Intro and Elim rules of N with a proof interpretation as is illustrated above with the &-rules.
	www.iep.utm.edu /l/logcon-d.htm (9103 words)

	Recent Work on Inference Rules
		The diverse inference rules were formulated with the objective of providing various types of reasoning capability.
		Every inference rule is required to be sound, yielding conclusions that follow logically and inevitably from the hypotheses in use.
		In Otter, factoring is implemented in two ways: as an inference rule as described in the preceding paragraph, and as a simplification rule, which applies when the conclusion is logically equivalent to the original clause.
	www-unix.mcs.anl.gov /AR/inf_rules.html (1090 words)

	2.8 Inference Rules (Site not responding. Last check: 2007-11-06)
		The rules with directory components in their targets are matched against the complete target name.
		If no rules match in Step #1, the rules without directory components in their targets are matched against the file name of the target, by default.
		When looking for an inference rule to build a target, the list is traversed from left to right with each extension being combined with the target extension to form the name of a suffix rule.
	www.agsrhichome.bnl.gov /Controls/doc/ClearCaseEnv/v4.0doc/cpf_4.0/ccase_nt/ccomake/ccomake-17.html (1372 words)

	Rule of inference (Site not responding. Last check: 2007-11-06)
		In the setting of formal logic (and many related areas), however, rules of inference are usually given in the following standard form:
		Rules of inference are usually formulated as rule schemata that encode (infinitely) many other rules.
		Rules of inference play a vital role in the specification of logical calculi as they are considered in proof theory, such as the sequent calculus.
	www.sciencedaily.com /encyclopedia/rule_of_inference (588 words)

	sair: Settings for Inference Rules
		The inference system consisting of all theses rules is refutationally complete In the case of dense orderings, one additionally needs to switch on variable elimination for refutational completeness, cf.
		The default setting is determined by the current theory and assures that sufficiently many inference rules are turned on.
		It is a good strategy (with respect to time efficiency) to set active inferences according to the problem at hand; for instance, for a purely equational problem only inference 3 (right superposition) is needed.
	www.mpi-sb.mpg.de /SATURATE/doc/Saturate/node49.html (142 words)

	New and old Leibniz
		The REALLY old Leibniz rule we got by fixing up the rule on the first page of chapter 3 (with our new meaning for textual substn., and also both a weak and a strong form -- weak for inputs and outputs real theorems, -- strong for inputs and outputs temporary theorems).
		But what I mean here by "old" Leibniz is really the generalization of that inference rule to the case where one has not biconditional (i.e., boolean "equal") theorems as premise and conclusion, but "equality" theorems involving expressions P, Q, etc. of arbitrary syntactic type.
		I believe we should really define "inference rules" and "theorems" at the same time, in an inductive definition of "theorem", as we did before in propositional logic.
	www.math.yorku.ca /Who/Faculty/Brettler/1090_f01/newoldLeib.html (1985 words)

	NMAKE Inference Rules (Site not responding. Last check: 2007-11-06)
		Inference rules supply commands to update targets and to infer dependents for targets.
		Extensions in an inference rule match a single target and dependent that have the same base name.
		Inference rules are user-defined or predefined; predefined rules can be redefined.
	www.compaq.com /fortran/docs/vf-html/pg/pg4nminf.htm (173 words)

	Inference Rules as a Parameter of Branch & Prune Algorithms (Site not responding. Last check: 2007-11-06)
		Inference Rules as a Parameter of Branch & Prune Algorithms
		In a wide variety of search algorithms, some form of inference is used to conclude that no feasible or optimal solution exists down a given branch of the search tree.
		We present general classes of inference rules for which inference can be run to completion in polynomial time.
	www.informs.org /Conf/NO95/TALKS/SE29.4.html (152 words)

	Inference Rules (Site not responding. Last check: 2007-11-06)
		Inference rules allow RDF Gateway to interpret the semantics that are described by one or more RDF schemas.
		This sample package defines a rule base (rdf_schema) that implements a couple of inference rules for RDF schemas (see include.rql).
		When these inference rules are included in a query RDF Gateway can semantically map between the classes and properties of the different RDF schemas.
	www.intellidimension.com /pages/site/packages/integrate/rules.rsp (159 words)

	Knowledge and Inference Rules (Site not responding. Last check: 2007-11-06)
		Knowledge rules, or declarative rules, state all the facts and relationships about a problem
		Inference rules, or procedural rules, advise on how to solve a problem, given that certain facts are known
		Inference rules become part of the inference engine
	web.usfca.edu /~villegas/classes/992-6275/6275ch14/sld025.htm (48 words)

	SHOE 1.01 Specification
		An ontology may declare one or more inferences which may be automatically made based on the relationship and category declarations found in marked-up SHOE text.
		Both the head and the body of an inference clause must contain at least one subclause; inference clauses with an empty head or body are incorrect and may be ignored.
		Inference clauses that do not meet these constraints are incorrect and may be ignored.
	www.cs.umd.edu /projects/plus/SHOE/spec.html (5483 words)

	Inference Rules (Site not responding. Last check: 2007-11-06)
		If this flag is set, the inference rule binary resolution (along with any other inference rules that are set) is used to generate new clauses.
		If this flag is set, the inference rule (positive) hyperresolution (along with any other inference rules that are set) is used to generate new clauses.
		If this flag is set, the inference rule negative hyperresolution (along with any other inference rules that are set) is used to generate new clauses.
	cay.cs.jcu.edu.au /%7Emarianne/otter/node41.html (243 words)

	Rules of Inference
		Each new step that we take in constructing a proof must then be a substitution-instance of one of these rules of inference.
		Thus, the inference is valid, and we can be sure that every argument that is a substitution-instance of this argument form must be valid.
		Since each step in our proof relies only upon a rule of inference and the supposed truth of earlier statements, the entire chain of reasoning must be valid.
	www.philosophypages.com /lg/e11a.htm (871 words)

	Schema
		A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema.
		Schemas are used in logic to specify rules of inference, in mathematics to describe theories with infinitely many axioms, and in semantics to give adequacy conditions for definitions of truth.
		In early twentieth-century formalizations of logic, it was common to use a substitution rule and a finite set of axioms instead of schemata.
	plato.stanford.edu /entries/schema (2127 words)

	[topicmapmail] Inference rules (Site not responding. Last check: 2007-11-06)
		It also includes an expanded analysis of how CGs relate to inferencing, which shows they are isomorphic to typed XTM associations.
		I conclude that only two new CTM ontologies are required, plus an open set of extensions for specific tools, applications and inference engines.
		Before CTM goes past early summaries and analysis, feedback from the readers of this current thread would be most welcome, especially on segment 2 - the part discussing facts and rules, and how CTM might standardize their notation under XTM 1.0 to match the popular strategies adopted in Conceptual Graphs.
	www.infoloom.com /pipermail/topicmapmail/2004q2/006090.html (282 words)

	BUG: Inference Rules Not Invoked on Multiple Targets (75206) (Site not responding. Last check: 2007-11-06)
		The Microsoft NMAKE utility may not invoke inference rules when multiple dependency lines are used for a single target as illustrated in the sample makefile below.
		When NMAKE processes the following sample makefile, the inference rule to build the executable file is not executed.
		However, the inference rule to build the object file is executed correctly because the object files are build as one target.
	www.sunsite.org.uk /sites/ftp.microsoft.com/MISC/KB/en-us/75/206.HTM (197 words)

	PRB: Spaces in Inference Rules Corrupt NMAKE Macro Expansion (65084) (Site not responding. Last check: 2007-11-06)
		A space has been inserted between the name of the target and the dependent extensions in an inference rule.
		In an inference rule, list the dependent file extension followed by the target file extension without any intervening embedded spaces.
		The following makefile examples demonstrate a few of the problems that can result when spaces are embedded in an inference rule.
	wwwtest.sunsite.org.uk /sites/ftp.microsoft.com/MISC/KB/en-us/65/084.HTM (157 words)

	Inference Rules (Site not responding. Last check: 2007-11-06)
		The inference rules are saved in a separate file.
		The inference engine is independent from the actual set of inference rules.
		The set of inference rules, together with information about the encodings of the items and the goal-items implement the information of the parsing schemata from chapter 4.
	www.dfki.de /~heckmann/diplom/Diplomarbeit/node58.html (137 words)

	Finding Shortest Proofs: An Application of Linked Inference Rules - Veroff (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		In this article we describe a procedure for systematically searching for shortest proofs in logical systems based on the inference rule condensed detachment.
		Although the procedure is exhaustive in nature{and therefore realistically is applicable only to relatively small problems{it is shown to overcome the obstacles to nding shortest proofs presented by ordinary resolution-style...
		The inference rule used is condensed detachment, encoded with a single clause of three literals and the use of hyperresolution....
	citeseer.ist.psu.edu /337795.html (455 words)

	Inference Rules. (Site not responding. Last check: 2007-11-06)
		Inference rules (or rules for short) are coded as functions from the proofs of the premises of a rule to its conclusion.
		Generally, the form of an inference rule is
		are provisos, that is, side conditions on the applicability of the rule
	www.cs.chalmers.se /~oloft/HTMLPapers/elp96/node12.html (99 words)

	Propositional Logic: inference rules (Site not responding. Last check: 2007-11-06)
		We'll use this list of valid inference rules as our definition, but, this is just one set of possible inference rules, and other people could use slightly different ones.
		Later, we'll often omit the description of exactly how the specific inference rule is used, since in many cases, that information is painfully obvious.
		Similarly, associativity of ∧ and ∨ are not among the inference rules.
	cnx.rice.edu /content/m10718/latest (1307 words)

	Basic Inference Rules for Algebraic and Coalgebraic Specifications - Padawitz (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: We give a survey of proof and computation rules, which, viewed from a long-standing experience with formal design methods, seem to be necessary and sucient for executing as well as verifying algebraic or coalgebraic data type speci cations.
		Based on many-sorted logics, swinging types [17, 21] provide the uniform syntax and the semantics with respect to which the set of rules is sound and, to a certain extent, complete.
		Basic inference rules for algebraic and coalgebraic specifications.
	citeseer.lcs.mit.edu /605893.html (466 words)

	Quick Ref - Inference Rules (Site not responding. Last check: 2007-11-06)
		Where Tp is the target prefix, Ts is the target suffix, Sp is the source prefix and Ss is the source suffix.
		When Make tries to match a target to an inference rule, each Tp%Ts pattern is matched against the target name, with "%" used to match zero or more characters.
		Every possible rule is tried and scored, with the best-scoring rule the one that uses "%" to match the smallest number of characters.
	www.opussoftware.com /quickref/Rules.htm (185 words)

	Inference Rules for Programming Languages with Side Effects in Expressions abstract (Site not responding. Last check: 2007-11-06)
		Paul E. Black and Phillip J. Windley, Inference Rules for Programming Languages with Side Effects in Expressions, Theorem Proving in Higher Order Logics: 9th International Conference (TPHOLs '96), Turku, Finland (August 1996), edited by Joakim von Wright, Jim Grundy, and John Harrison, Springer-Verlag, Berlin, Germany, 1996, pages 51-60.
		We present inference rules for assignment statements with pre- and post-evaluation side effects and
		We also discuss the need to abstract the semantics of program functions and present an inference rule for abstraction.
	hissa.nist.gov /~black/Papers/hol96.html (178 words)

	Science Forums - Fundamentals of Logic
		It even has Lewis Carrol's amusing spoof on modus ponens, which illustrates what you said, we don't prove the inference rules, they are obviously reasonable and that's that, so we use them.
		There is also the related matter of formal systems which do include the inference rules of logic but add one or more axioms as well.
		Change this, or change the inference rules, and you are talking about a different formal system, e.
	www.scienceforums.com /archive/index.php/t-2421.html (3758 words)

	Creating Inference Rules for Nonstandard File Extensions (81454) (Site not responding. Last check: 2007-11-06)
		If you use NMAKE to create an Inference Rule for a file with a nonstandard file extension (for example, an extension other than.ASM,.BAS,.C, and so forth), you must specify the extension in the.SUFFIXES list in the makefile.
		It is sometimes necessary or desirable to compile a source file that has a nonstandard file extension.
		To compile this file with NMAKE, you must create a new inference rule for that extension.
	www.sunsite.org.uk /sites/ftp.microsoft.com/MISC/KB/en-us/81/454.HTM (211 words)

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