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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 ..."
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Cited by 100 (6 self)
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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 . . . . . . . . . . . . . . . . . . . . . ...
Specifying and Implementing Theorem Provers in a HigherOrder Logic Programming Language
, 1989
"... We argue that a logic programming language with a higherorder intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. The language extends traditional logic programming languages by replacing firstorder terms with simplytyped λterms, replacing ..."
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Cited by 46 (7 self)
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We argue that a logic programming language with a higherorder intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. The language extends traditional logic programming languages by replacing firstorder terms with simplytyped λterms, replacing firstorder unification with higherorder unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of proof systems can be naturally specified in this language. The higherorder features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many proof systems. In addition, abstraction in metaterms allows the construction of terms representing object level proofs which capture the notions of abstractions found in many proof systems. The operational interpretations of the connectives of the language provide a set of basic search operations which describe goaldirected search for proofs. To emphasize the generality of the metalanguage, we compare it to another general specification language: the Logical Framework (LF). We describe a translation which compiles a specification of a logic in LF to a set of formulas of our metalanguage, and
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 ..."
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Cited by 44 (16 self)
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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,
Set Theory for Verification: II  Induction and Recursion
 Journal of Automated Reasoning
, 2000
"... A theory of recursive definitions has been mechanized in Isabelle's ZermeloFraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning. ..."
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Cited by 41 (19 self)
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A theory of recursive definitions has been mechanized in Isabelle's ZermeloFraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning.
Taxonomic Syntax for First Order Inference
 Journal of the ACM
, 1989
"... Most knowledge representation languages are based on classes and taxonomic relationships between classes. Taxonomic hierarchies without defaults or exceptions are semantically equivalent to a collection of formulas in first or der predicate calculus. Although designers of knowledge representation l ..."
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Cited by 36 (13 self)
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Most knowledge representation languages are based on classes and taxonomic relationships between classes. Taxonomic hierarchies without defaults or exceptions are semantically equivalent to a collection of formulas in first or der predicate calculus. Although designers of knowledge representation lan guages often express an intuitive feeling that there must be some advantage to representing facts as taxonomic relationships rather than first order for mulas, there are few,, if any, technical results supporting this intuition. We attempt to remedy this situation by presenting a taxonomic syntax for first order predicate calculus and a series of theorems that support the claim that taxonomic syntax is superior to classical syntax.
Type inference and semiunification
 In Proceedings of the ACM Conference on LISP and Functional Programming (LFP ) (Snowbird
, 1988
"... In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically type ..."
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Cited by 25 (6 self)
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In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically typed languages (Algol68, Pascal). These polymorphic languages can be type checked at compile time, yet allow functions whose arguments range over a variety of types. We investigate several polymorphic type systems, the most powerful of which, termed MilnerMycroft Calculus, extends the socalled letpolymorphism found in, e.g., ML with a polymorphic typing rule for recursive definitions. We show that semiunification, the problem of solving inequalities over firstorder terms, characterizes type checking in the MilnerMycroft Calculus to polynomial time, even in the restricted case where nested definitions are disallowed. This permits us to extend some infeasibility results for related combinatorial problems to type inference and to correct several claims and statements in the literature. We prove the existence of unique most general solutions of term inequalities, called most general semiunifiers, and present an algorithm for computing them that terminates for all known inputs due to a novel “extended occurs check”. We conjecture this algorithm to be
Engineering User Models to Enhance Multimodal Dialogue
, 1992
"... An extension of the GUMS user modelling module is described which includes multiple inheritance between user stereotypes, multiple top level nodes in a network to allow a range of dimensions on which the user can be classified, and rules to change the stereotypes of users. A method is described usin ..."
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Cited by 14 (11 self)
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An extension of the GUMS user modelling module is described which includes multiple inheritance between user stereotypes, multiple top level nodes in a network to allow a range of dimensions on which the user can be classified, and rules to change the stereotypes of users. A method is described using Wizard of Oz studies and interviews to provide the information to populate this model for applications and to provide rules to recognise which stereotypes apply to users. The use of the method and the user modelling module are illustrated for a human computer interface which supports multimodal dialogue. The resulting cooperative dialogue with this interface is compared with the facilities offered by more complex alternative modelling approaches. Keyword Codes: H.1.2; I.2.4; H.5.2 Keywords: User/Machine Systems; Knowledge Representation Formalisms and Methods; User Interfaces 1. INTRODUCTION It is generally accepted that complex user interfaces should be tailorable to individual users. ...
A Constraintbased Partial Evaluator for Functional Logic Programs and its Application
, 1998
"... The aim of this work is the development and application of a partial evaluation procedure for rewritingbased functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewritingbased computational model extends traditional functional ..."
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Cited by 12 (0 self)
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The aim of this work is the development and application of a partial evaluation procedure for rewritingbased functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewritingbased computational model extends traditional functional programming languages by incorporating logical features, including logical variables and builtin search, into its framework. This work is the first to address the automatic specialisation of these functional logic programs. In particular, a theoretical framework for the partial evaluation of rewritingbased functional logic programs is defined and its correctness is established. Then, an algorithm is formalised which incorporates the theoretical framework for the procedure in a fully automatic technique. Constraint solving is used to represent additional information about the terms encountered during the transformation in order to improve the efficiency and size of the residual programs. ...
Interest driven suppositional reasoning
 Journal of Automated Reasoning
, 1990
"... Abstract. The aim of this paper is to investigate two related aspects of human reasoning, and use the results to construct an automated theorem prover for the predicate calculus that at least approximately models human reasoning. The result is a nonresolution theorem prover that does not use Skolem ..."
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Cited by 11 (3 self)
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Abstract. The aim of this paper is to investigate two related aspects of human reasoning, and use the results to construct an automated theorem prover for the predicate calculus that at least approximately models human reasoning. The result is a nonresolution theorem prover that does not use Skolemization. It involves two central ideas. One is the interest constraints that are of central importance in guiding human reasoning. The other is the notion of suppositional reasoning, wherein one makes a supposition, draws inferences that depend upon that supposition, and then infers a conclusion that does not depend upon it. Suppositional reasoning is involved in the use of conditionals and reductio ad absurdum, and is central to human reasoning with quantifiers. The resulting theorem prover turns out to be surprisingly efficient, beating most resolution theorem provers on some hard problems.
SIMBA: Belief Ascription by Way of Simulative Reasoning
, 1996
"... A key cognitive faculty that enables humans to communicate with each other is their ability to incrementally construct and use models describing the mental states of others, in particular, models of their beliefs. Not only do humans have beliefs about the beliefs of others, they can also reason with ..."
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Cited by 8 (0 self)
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A key cognitive faculty that enables humans to communicate with each other is their ability to incrementally construct and use models describing the mental states of others, in particular, models of their beliefs. Not only do humans have beliefs about the beliefs of others, they can also reason with these beliefs even if they do not hold them themselves. If we want to build an artificial or computational cognitive agent that is similarly capable, we need a formalism that is fully adequate to represent the beliefs of other agents, and that also specifies how to reason with them. Standard formalizations of knowledge or belief, in particular the various epistemic and doxastic logics, seem to be not very well suited to serve as the formal device upon which to build an actual computational agent. They neglect either representation problems, or the reasoning aspect, or the defeasibility that is inherent in reasoning about somebody else's beliefs, or they use idealizations which are problema...