Results 1  10
of
73
The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
Abstract

Cited by 100 (6 self)
 Add to MetaCart
This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
On Generating Small Clause Normal Forms
, 1998
"... In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and refined Skolemization methods. We illustrate their effect on various examples. By an exhaustive experiment of all firstorder TPTP problems, it shows that our clause normal form tran ..."
Abstract

Cited by 90 (2 self)
 Add to MetaCart
In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and refined Skolemization methods. We illustrate their effect on various examples. By an exhaustive experiment of all firstorder TPTP problems, it shows that our clause normal form transformation yields fewer clauses and fewer literals than the methods known and used so far. This often allows for exponentially shorter proofs and, in some cases, it makes it even possible for a theorem prover to find a proof where it was unable to do so with more standard clause normal form transformations. 1
leanTAP: Lean Tableaubased Deduction
 Journal of Automated Reasoning
, 1995
"... . "prove((E,F),A,B,C,D) : !, prove(E,[FA],B,C,D). prove((E;F),A,B,C,D) : !, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) : !, "+length(C,D), copyterm((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[GC],D). prove(A,,[CD],,) : ((A= (B); (A)=B)) ? (unify(B,C); pro ..."
Abstract

Cited by 78 (11 self)
 Add to MetaCart
. "prove((E,F),A,B,C,D) : !, prove(E,[FA],B,C,D). prove((E;F),A,B,C,D) : !, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) : !, "+length(C,D), copyterm((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[GC],D). prove(A,,[CD],,) : ((A= (B); (A)=B)) ? (unify(B,C); prove(A,[],D,,)). prove(A,[EF],B,C,D) : prove(E,F,[AB],C,D)." implements a firstorder theorem prover based on freevariable semantic tableaux. It is complete, sound, and efficient. 1 Introduction The Prolog program listed in the abstract implements a complete and sound theorem prover for firstorder logic; it is based on freevariable semantic tableaux (Fitting, 1990). We call this lean deduction: the idea is to achieve maximal efficiency from minimal means. We will see that the above program is indeed very efficientnot although but because it is extremely short and compact. Our approach surely does not lead to a deduction system which is superior to highly sophisticated systems li...
The Value of the Four Values
 Artificial Intelligence
, 1998
"... In his wellknown paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the fourvalued structure has among Ginsberg's wellknown bilatti ..."
Abstract

Cited by 62 (6 self)
 Add to MetaCart
In his wellknown paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the fourvalued structure has among Ginsberg's wellknown bilattices is similar to the role that the twovalued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilatticevalued logics can actually be characterized as fourvalued inference relations. In addition, we compare the use of threevalued logics with the use of fourvalued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter. Keyworkds: Bilattices, Paraconsistency, Multiplevalued systems, Preferential logics, Reasoning. 1 Introduction In [Be77a, Be77b] Belnap introduced a logic intended to deal in a useful way with inconsistent and incomplete information....
SPASS FLOTTER Version 0.42
"... t represents the sort restrictions on the variables. There are two extra inference rules which transform the sort constraint into solved form: Sort resolution and empty sort. These rules 1 The name is the result of a lunch break, FLOTTER means "faster", in German. 2 Synergetic Prover Augmenting ..."
Abstract

Cited by 54 (3 self)
 Add to MetaCart
t represents the sort restrictions on the variables. There are two extra inference rules which transform the sort constraint into solved form: Sort resolution and empty sort. These rules 1 The name is the result of a lunch break, FLOTTER means "faster", in German. 2 Synergetic Prover Augmenting Superposition with Sorts, SPASS means "fun", in German. implement a specific strategy of the sorted unification algorithm [15] on the sort constraint literals. In addition to these inference rules, SPASS includes a splitting rule. The splitting rule is a variant of the usual firule of tableau. If SPASS splits a clause into two different cases, the two parts will not share variables, i.e. these parts can independently be refuted. For SPASS we implemented powerful reduction rules: tautology deletion, subsumption, condensing, an efficient variant of contextual rewriting,
Set theory for verification: I. From foundations to functions
 J. Auto. Reas
, 1993
"... A logic for specification and verification is derived from the axioms of ZermeloFraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higherord ..."
Abstract

Cited by 46 (18 self)
 Add to MetaCart
A logic for specification and verification is derived from the axioms of ZermeloFraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higherorder syntax supports the definition of new binding operators. Unknowns in subgoals can be instantiated incrementally. The paper describes the derivation of rules for descriptions, relations and functions, and discusses interactive proofs of Cantor’s Theorem, the Composition of Homomorphisms challenge [9], and Ramsey’s Theorem [5]. A generic proof assistant can stand up against provers dedicated to particular logics. Key words. Isabelle, set theory, generic theorem proving, Ramsey’s Theorem,
A Benchmark Method for the Propositional Modal Logics K, KT, S4
, 1996
"... A lot of methods have been proposed (and sometimes implemented) for proof search in the propositional modal logics K, KT, and S4. It is difficult to compare the usefulness of these methods in practice, since mostly only the execution times for a few simple formulas have been published. We try to imp ..."
Abstract

Cited by 44 (1 self)
 Add to MetaCart
A lot of methods have been proposed (and sometimes implemented) for proof search in the propositional modal logics K, KT, and S4. It is difficult to compare the usefulness of these methods in practice, since mostly only the execution times for a few simple formulas have been published. We try to improve this unsatisfactory situation by presenting a set of benchmark formulas. Note that we do not just list formulas, but give a method that allows to compare different provers today and in the future. As a starting point we give the results we obtained when we applied this benchmark method to the Logics Workbench (LWB). Moreover we hope that the discussion of postulates concerning benchmark tests for automated theorem provers help to obtain improved benchmark methods for other logics, too.
A generic tableau prover and its integration with Isabelle
 Journal of Universal Computer Science
, 1999
"... Abstract: A generic tableau prover has been implemented and integrated with Isabelle [Paulson, 1994]. Compared with classical rstorder logic provers, it has numerous extensions that allow it to reason with any supplied set of tableau rules. It has a higherorder syntax in order to support userde ne ..."
Abstract

Cited by 38 (10 self)
 Add to MetaCart
Abstract: A generic tableau prover has been implemented and integrated with Isabelle [Paulson, 1994]. Compared with classical rstorder logic provers, it has numerous extensions that allow it to reason with any supplied set of tableau rules. It has a higherorder syntax in order to support userde ned binding operators, such as those of set theory. The uni cation algorithm is rstorder instead of higherorder, but it includes modi cations to handle bound variables. The proof, when found, is returned to Isabelle as a list of tactics. Because Isabelle veri es the proof, the prover can cut corners for e ciency's sake without compromising soundness. For example, the prover can use type information to guide the search without storing type information in full. Categories: F.4, I.1