First-order resolution

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Topic: First-order resolution

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	first order predicate logic
		First order predicate logic makes a stronger set of ontological Commitments (what sort of entities exists in UoD)than Propositional logic(which deals only with facts).The main one is that the world consists of objects, that is things with individual identities and properties that distinguish them from other objects.
		First step before resolution can be applied to a set of formulae it is required to covert the given formulae into to what is known as clausal form.
		Resolution: The resolution proof method is a uniform proof method in the sense that all formulas are converted to particular regular form called the ‘clausal form’ involving disjunctions,conjuctions and negations of sub-formulas only.
	guthulamurali.freeservers.com /pl.html

	CATHOLIC ENCYCLOPEDIA: Order of Preachers
		At all events the interior troubles of the order grew out of the difficulty of maintaining the nice equilibrium which the first legislators established, and which was preserved to a remarkable degree during the first century of the order's existence.
		The first Dominican doctors, who came from the universities into the order, or who taught in the universities, adhered for a long time to the Augustinian doctrine.
		The same solicitude to remove the order from the odium of the inquisitorial office impelled the provincial chapter of Cahors (1244) to forbid that anything should accrue to the friars from the administration of the Inquisition, that the order might not be slandered.
	www.newadvent.org /cathen/12354c.htm

	First Order Predicate Calculus Theorem Prover
		THEOREM PROVER FOR THE FIRST ORDER PREDICATE CALCULUS.
		THEOREMS IN THE FIRST ORDER PREDICATE CALCULUS THAT ARE TO BE PROVED?
		THE "RESOLUTION PRINCIPLE" IS USED AS THE BASIC MECHANISM.
	www.frobenius.com /theorem.htm

	Citations: Tree-based heuristics in modal theorem proving - Areces, Gennari, Heguiabehere, de Rijke (ResearchIndex)
		The latter approach works nicely with resolution based first order theorem prover, which can be Authors supported in part by NSF grants CCR 9988322, CCR 0124077, IIS 9908435, IIS9978135, and EIA 0086264, by BSF grant 9800096, and by a grant from the Intel Corporation.
		The latter approach works nicely with a resolution based first order theorem prover, which can be used as a decision procedure for modal satisfiability by using appropriate resolution strategies [16] Other approaches for modal satisfiability such as mosaics, type elimination, Supported in....
		First we encode modal input formulas into layers of finite constraint satisfaction problems (CSPs) with more values than just the Boolean ones; then we show that any complete constraint solver for finite CSPs can be used to solve them, and, hence, to determine modal satisfiability, in stead of....
	citeseer.csail.mit.edu /context/1510175/407484

	G.Dowek: Automated Theorem Proving in First-order Logic Modulo
		On the other hand, higher-order logic, also called simple type theory, can be expressed as a first-order theory H, and first-order theorem proving methods, such as first-order resolution, can be used for this theory.
		First, the first-order unification algorithm has to be replaced by the higher-order one.
		However, we can try to understand higher-order resolution as a special automated theorem proving method designed for the theory H.
	www.logic.at /ftp98/dowek.html

	Resolution_based_inference_engines.doc
		Ordered resolution: this is the way prolog operates; the clauses are treated from the first to the last and each single clause is unified from left to right.
		If the empty clause is produced, then the theorem T logically follows from the set of axioms A. Resolution is refutation complete for first order logic: if a contradiction exists it will be found.
		Resolution strategies [UMBC] Breadth first Set of support: at least one parent clause must be from the negation of the goal or one of the “descendents” of such a goal clause.
	www.agfa.com /w3c/2002/02/thesis/Resolution_based_inference_engines.doc

	Citations: Symbolic logic and mechanical theorem proving - Chang, Lee (ResearchIndex)
		can be used in the setting of first order logic to generate the instances for a goal literal by building a proof of the goal from the clauses, and applying the resulting substitutions to the goal.
		First order logic is the domain of most of traditional machine oriented theorem provers.
		Once the negation of a formula is translated into this form, the resolution inference rule is applied in order to find a proof of the....
	citeseer.csail.mit.edu /context/101125/0

	Resolution Theorem Proving
		The statements are shown in English (top), in conjunctive normal form (middle and indented), and in the syntax of First Order Logic (bottom and most indented).
		(Robinson, 1965) is one proof theoretic method for proving theorems in First Order Logic (FOL).
		Resolution theorem proving works by negating the assertion that is to be proved, and trying to prove a contradiction...or the empty set.
	www.rci.rutgers.edu /~cfs/472_html/Logic_KR/resolution.html

	Definition of index.php?search=order&limit=20&offset=20
		1:...gic]] and [[automated theorem proving]], '''first- order resolution''' is a [[theorem]]-[[proofproving]]...
		The Order was first authorized by order of King [[William I of the NetherlandsWilliam I]...
		of all [[real number]]s, one can assert in first- order logic the existence of an additive inverse of eac...
	www.wordiq.com /knowledge/index.php?search=order&limit=20&offset=20

	First-order resolution - Wikipedia, the free encyclopedia
		automated theorem proving, first-order resolution is a theorem- proving technique.
		So the question is, how does the resolution technique derive the last clause from the first two?
		To recast the reasoning using the resolution technique, first the clauses must be converted to
	en.wikipedia.org /wiki/First_order_resolution

	Prolog
		The first case is an example of a definition in Verb Subject Object order, and the second of Verb Object Subject order.
		However in the first case, Sally comes first in the argument list, and in the second, Pat comes first (the order in the argument list matters).
		The entirety of a list can be processed by processing the first element, and then the rest of the list, in a recursive manner.
	www.sciencedaily.com /encyclopedia/prolog

	Analysis Guide for Chandra High Resolution Spectroscopy
		Higher-order grids are obtained by dividing the first order value by the order.
		If the value is within the CCD resolution of an integer value, then that integer value is assigned as the order.
		The spacecraft pointing is intentionally ``dithered'' in order to spread signal over large regions, relative to a detector pixel, since the PSF is comparable to a pixel, but the efficiency calibration has a larger scale.
	space.mit.edu /ASC/analysis/AGfCHRS/AGfCHRS.html

	Resolution - Wikipedia, the free encyclopedia
		First-order resolution, a proof procedure for First-Order-Logic introduced by Robinson.
		Resolution class submarines, the UK's first nuclear missile submarines
		projective resolutions and exact resolutions are certain series in mathematics
	en.wikipedia.org /wiki/Resolution

	Towards Modular Access to Electronic Handbooks: Caracciolo: JoDI
		The first set of experiments will assess how the structure and interface of the LoLa concept hierarchy are exploited by the users.
		Once this first task has been performed, and after having linked the concept hierarchy to the handbook, we will assess the effectiveness of the hierarchy for the disclosure of the text.
		Provided that the siblings are listed in some meaningful order, they prevent the "lost in space" problem.
	jodi.ecs.soton.ac.uk /Articles/v03/i04/Caracciolo

	Deduction Modulo
		Moreover as we stay in a first-order setting, extensions, such as equational higher-order resolution, may be easier to handle.
		Hence expressing higher-order logic as a first-order theory and applying a first-order proof search method is at least as efficient as a direct implementation.
		The first contribution of this paper is to define a {\em sequent calculus modulo} that gives a proof theoretic account of the combination of computations and deductions.
	www.loria.fr /%7Eckirchne/=tpm/TPM.html

	Inference in First Order Logic I
		First order logic builds on simple propositional logic by adding objects, predicates, variables and quantifiers.
		Inference in First Order Logic (Sections 9.1 to 9.4 of Stuart Russel and Pete Norvig (1995).
		First off we need to convert the sentences to predicate logic symbols.
	sern.ucalgary.ca /courses/CPSC/533/W99/presentations/L1_9A_Chow_Low/main.html

	Inference in First Order Logic: Resolution
		This is because there may be nothing in the database for resolution to be applied to, even though the query is valid.
		Notice we reduce the number of atoms by one on one side of each implication when we apply the resolution rule.
		Simple resolution (propositional logic) can be viewed as
	www.sdsc.edu /~tbailey/teaching/cse151/lectures/chap09b.html

	From Logic to Logic Programming (Foundations of Computing): Current Amazon U.S.A. One-Edition Data
		Doets provides a novel approach to resolution that is applied to the first-order case and the case of (positive) logic programs.
		A mathematically oriented introduction to the theory of logic programming that presents a systematic exposition of the resolution methods for propositional, first-order, and Horn-clause logics, together with an analysis of the semantic aspects of the method.
		This mathematically oriented introduction to the theory of logic programming presents a systematic exposition of the resolution method for propositional, first-order, and Horn- clause logics, together with an analysis of the semantic aspects of the method.
	www.1-brs.com /us-reviewed/0262041421.html

	Selected Publications of Hans de Nivelle
		This makes it possible to translate the output of a resolution theorem prover into a purely first-order proof that is moderate in size.
		The resolution game is a game that can be played between two players, based on a set of ordered clauses.
		This paper introduces the resolution game and proves the completeness of resolution with orders that are descending.
	www.mpi-sb.mpg.de /~nivelle/publications

	CIS587 : LOGIC, PART 2
		Theorem: First Order Logic, with the Resolution Inference Rule, is sound and refutation complete.
		First we introduce Resolution in the Propositional Calculus, that is, in a language with only truth valued variables.
		The algorithm for Binary Resolution is here, and the corresponding lisp code is here.
	www.cis.temple.edu /~ingargio/cis587/readings/logic2.html

	Joe Hurd: Research: Automatic First-Order Proof
		A secondary result of this research is a flexible interface between higher-order and first-order logic, allowing arbitrary clausal refutations to be automatically lifted to higher-order logic theorems.
		First-order problems often turn up during proof in an interactive theorem prover, and it's extremely convenient to simply hand them off to an automatic prover.
		to do just this in HOL, and the objective of this research is to use the resolution calculus to create more powerful tactics.
	www.cl.cam.ac.uk /users/jeh1004/research/metis

	Computer Science - CS 251 Logical Structures (4 credits)
		Describe the resolution inference rule; use it to write formal proofs in first-order logic; and describe how resolution is used to execute a logic program.
		Predicate Logic: first order predicate calculus, formal reasoning.
		Applied Logic: proving programs correct, higher order logics.
	www.cs.pdx.edu /course.php?cid=15

	Schmidt and Hustadt (2000a)
		We show that this class is decidable by an ordering refinement of first-order resolution and a new form of dynamic renaming, called separation.
		Fluted logic is a fragment of first-order logic without function symbols in which the arguments of atomic subformulae form ordered sequences.
		Our characterisation of fluted logic is in terms of a new class of so-called fluted clauses.
	www.cs.man.ac.uk /~schmidt/publications/SchmidtHustadt00a.html

	UL CS Technical Reports
		The method is based on classical first-order resolution and can, thus, be efficiently implemented.
		We first define a normal form for monodic formulae and show how arbitrary monodic formulae can be translated into the normal form, while preserving satisfiability.
		We then introduce novel resolution calculi that can be applied to formulae in this normal form and state correctness and completeness results for the method.
	www.csc.liv.ac.uk /research/techreports/tr2003/tr03005abs.html

	Playing first-order logic
		The first task is to convert this rather "rich" language to an equivalent simpler one, where the knowledge base is a list of clauses (implicitly joined with "and") and each clause is a list of (possibly negated) simple predicates, implicitly joined by "or".
		Come time, I will have to add the "real" meat, Skolemized variables and functions, but first Felix must be proven to eat fish...
		if 0 {Now the core of proving, the resolution rule where two rules from KB make a new one, which is shorter than just concatenating the two, because a pair of contradicting terms is cancelled out:}
	wiki.tcl.tk /3378.html

	Course Notes on First Order Logic
		The importance of the compactness theorem in establishing the expressive weakness of first order logic is emphasized.
		This node contains two installments of the notes describing basic results on first order logic.
		It is then shown how the completeness of resolution implies the compactness theorem.
	www.autoreason.com /notes/fol.html

	FTP'2000
		The workshop welcomes original contributions on theorem proving in first-order classical, many-valued, and modal logics, including nonexclusively: resolution, equational reasoning, term-rewriting, model construction, constraint reasoning, unification, propositional logic, specialized decision procedures; strategies and complexity of theorem proving procedures; implementation techniques and applications of first-order theorem provers to problems in verification, artificial intelligence, and mathematics.
		FTP'2000 is the third in a series of workshops intended to focus effort on First-Order Theorem Proving as a core theme of Automated Deduction, and to provide a forum for presentation of very recent work and discussion of research in progress.
		Please ask Peter Baumgartner or Roy Dyckhoff in order to get one.
	www.uni-koblenz.de /ftp00

	Inductive Theorem Prover INKA 4.0
		The system possesses a powerful predicate-logic prover component which (as already mentioned) is based on an order- sorted variant of a resolution calculus with paramodulation.
		The INKA-system 4.0 is a first-order theorem prover with induction which is based on the explicit induction paradigm.
		In order to make the use of the INKA system in practical applications more comfortable, certain predefined data types are at hand together with special built-in procedures for their treatment.
	www.dfki.de /vse/systems/inka

	order: first order logic
		Who do who close easy expressiveness definable unification equivalences first order logic, lukasiewicz equivalences henkin resolution lpl refutation categorical if and only if logician.
		Hoare life name sure oline elimination intensional resolution formalization first order logic, unary completeness predicate calculus logica kleene hoare sentential skolem predicat.
		Paradoxes money went when between gurevich herbrand unary monadic first order logic, setheo graham priest paradoxes stanford encyclopedia of philosophy inference intensional coq prolog theorem.
	order10.blogspot.com /2004/12/first-order-logic.html

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Topic: First-order resolution

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