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Ivy: A Preprocessor And Proof Checker For FirstOrder Logic
, 1999
"... This case study shows how nonACL2 programs can be combined with ACL2 functions in such a way that useful properties can be proved about the composite programs. Nothing is proved about the nonACL2 programs. Instead, the results of the nonACL2 programs are checked at run time by ACL2 functions, and ..."
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Cited by 38 (10 self)
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This case study shows how nonACL2 programs can be combined with ACL2 functions in such a way that useful properties can be proved about the composite programs. Nothing is proved about the nonACL2 programs. Instead, the results of the nonACL2 programs are checked at run time by ACL2 functions, and properties of these checker functions are proved. The application is resolution/paramodulation automated theorem proving for firstorder logic. The top ACL2 function takes a conjecture, preprocesses the conjecture, and calls a nonACL2 program to search for a proof or countermodel. If the nonACL2 program succeeds, ACL2 functions check the proof or countermodel. The top ACL2 function is proved sound with respect to finite interpretations. Introduction Our ACL2 project arose from a different kind of automated theorem proving. We work with fully automatic resolution/paramodulation theo This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram...
Modality in Dialogue: Planning, Pragmatics and Computation
, 1998
"... Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the ..."
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Cited by 37 (9 self)
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Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the domain and the states of knowledge of the participants in the conversation. This dissertation shows how such characterizations can be specified declaratively and accessed efficiently in NLG. The heart of this dissertation is a study of logical statements about knowledge and action in modal logic. By investigating the prooftheory of modal logic from a logic programming point of view, I show how many kinds of modal statements can be seen as straightforward instructions for computationally manageable search, just as Prolog clauses can. These modal statements provide sufficient expressive resources for an NLG system to represent the effects of actions in the world or to model an addressee whose knowledge in some respects exceeds and in other respects falls short of its own. To illustrate the use of such statements, I describe how the SPUD sentence planner exploits a modal knowledge base to
Computing finite models by reduction to functionfree clause logic
 Journal of Applied Logic
, 2007
"... Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT sol ..."
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Cited by 34 (9 self)
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Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT solvers to them. A problem with this method is that it does not scale well because the propositional formulas to be considered may become very large. We propose instead to reduce model search to a sequence of satisfiability problems consisting of functionfree firstorder clause sets, and to apply (efficient) theorem provers capable of deciding such problems. The main appeal of this method is that firstorder clause sets grow more slowly than their propositional counterparts, thus allowing for more space efficient reasoning. In this paper we describe our proposed reduction in detail and discuss how it is integrated into the Darwin prover, our implementation of the Model Evolution calculus. The results are general, however, as our approach can be used in principle with any system that decides the satisfiability of functionfree firstorder clause sets. To demonstrate its practical feasibility, we tested our approach on all satisfiable problems from the TPTP library. Our methods can solve a significant subset of these problems, which overlaps but is not included in the subset of problems solvable by stateoftheart finite model builders such as Paradox and Mace4.
Automated Theorem Proving in Software Engineering
"... Introduction. The quickly rising amount and complexity of developed and used software require more and more a rigorous application of formal methods during the entire software life cycle. Points of particular interest include: specification and its refinements, program synthesis, software reuse, sup ..."
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Cited by 31 (3 self)
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Introduction. The quickly rising amount and complexity of developed and used software require more and more a rigorous application of formal methods during the entire software life cycle. Points of particular interest include: specification and its refinements, program synthesis, software reuse, support for testing and debugging, software reengineering, and software/hardware codesign (e.g., [16]). Wherever formal methods are applied, proof tasks of most different size and complexity arise in large quantities. Traditionally, interactive theorem provers (e.g., PVS, KIV, HOL, Isabelle) are being used to tackle those proof tasks. These systems have a highly expressive input language (mostly higher order logic), but in general many interactions by an expert user have to be performed for each proof task. Interactive theorem provers (ITPs) are just too interactive. On the other hand, Model Checkers (for propositional (temporal) logic; e.g., SMV [1]) are more and more used in the area
Generic Automatic Proof Tools
, 1997
"... This article explores a synthesis between two distinct traditions in automated reasoning: resolution and interaction. In particular it discusses Isabelle, an interactive theorem prover based upon a form of resolution. It aims to demonstrate the value of proof tools that, compared with traditional re ..."
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Cited by 29 (11 self)
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This article explores a synthesis between two distinct traditions in automated reasoning: resolution and interaction. In particular it discusses Isabelle, an interactive theorem prover based upon a form of resolution. It aims to demonstrate the value of proof tools that, compared with traditional resolution systems, seem absurdly limited. Isabelle's classical reasoner searches for proofs using a tableau approach. The reasoner is generic: it accepts rules proved in applied theories, involving defined connectives. The reasoner works in a variety of domains without reducing them to firstorder logic. Resolution systems such as Otter [13], setheo [11] and pttp [34] represent automatic theorem proving at its highest point of refinement. They achieve extremely high inference rates and can run continuously for days without running out of storage. They can crack many of the toughest challenge problems that have been circulated. While they exploit many specialized algorithms, data structures and optimizations, they rely crucially on unification. Interactive systems let the user direct each step of the proof. They can implement complicated formalisms, chosen for maximum expressiveness, and typically based on the typed calculus. hol [7, 8] and pvs [23] are used for verification of hardware and realtime systems, while Coq [4] is used for formalizing mathematics. Large numbers of axioms  say, the description of a cpu design  do not overwhelm them, because finding the proof is the user's job. Partial automation is sometimes provided, but a resolution enthusiast would regret the lack of uniform search procedures based on unification. One procedure provided by most interactive provers is rewriting. Rewrite rules have many advantages. Unlike programmed inference rules, they are ...
leanCoP: Lean ConnectionBased Theorem Proving
 UNIVERSITY OF KOBLENZ
, 2000
"... The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); len ..."
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Cited by 29 (9 self)
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The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); length(P,K), K!I, append(R,[DQ],S)), prove(F,S,[LP],I)), prove(C,M,P,I)." implements a theorem prover for classical firstorder (clausal) logic which is based on the connection calculus. It is sound, complete (if one more line is added), and demonstrates a comparatively strong performance.
Solving Open Questions and Other Challenge Problems Using Proof Sketches
, 2001
"... . In this article, we describe a set of procedures and strategies for searching for proofs in logical systems based on the inference rule condensed detachment. The procedures and strategies rely on the derivation of proof sketchessequences of formulas that are used as hints to guide the search for ..."
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Cited by 28 (13 self)
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. In this article, we describe a set of procedures and strategies for searching for proofs in logical systems based on the inference rule condensed detachment. The procedures and strategies rely on the derivation of proof sketchessequences of formulas that are used as hints to guide the search for sound proofs. In the simplest case, a proof sketch consists of a subproofkey lemmas to prove, for exampleand the proof is completed by lling in the missing steps. In the more general case, a proof sketch consists of a sequence of formulas sucient to nd a proof, but it may include formulas that are not provable in the current theory. We nd that even in this more general case, proof sketches can provide valuable guidance in nding sound proofs. Proof sketches have been used successfully for numerous problems coming from a variety of problem areas. We have, for example, used proof sketches to nd several new twoaxiom systems for Boolean algebra using the Sheer stroke. Keywords: proof sk...
Automatic Proofs and Counterexamples for Some Ortholattice Identities
 Information Processing Letters
, 1998
"... This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, ..."
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Cited by 25 (2 self)
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This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill. Keywords: Automatic theorem proving, ortholattice, quantum logic, theory of computation. 1 Introduction An ortholattice is an algebra with a binary operation (join) and a unary operation 0 (complement) satisfying the following (independent) set of identities. x y = (x 0 y 0 ) 0 (definition of meet) x y = y x (x y) z = x (y z) x (x y) = x x 00 = x x (y y 0 ) = y y 0 Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W31109Eng38. From these identities one can...