Results 1  10
of
26
tps: A theorem proving system for classical type theory
 Journal of Automated Reasoning
, 1996
"... This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
Abstract

Cited by 71 (6 self)
 Add to MetaCart
This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems which TPS can prove completely automatically are given to illustrate certain aspects of TPS’s behavior and problems of theorem proving in higherorder logic. 7
Naming proofs in classical propositional logic
 IN PAWE̷L URZYCZYN, EDITOR, TYPED LAMBDA CALCULI AND APPLICATIONS, TLCA 2005, VOLUME 3461 OF LECTURE
"... We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentiali ..."
Abstract

Cited by 24 (8 self)
 Add to MetaCart
We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cutelimination procedure. This gives us a “Boolean ” category, which is not a poset. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a “real” sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures.
Equality Reasoning in SequentBased Calculi
 Handbook of Automated Reasoning, volume I, chapter 10
, 1996
"... Contents i Introduction ........................................ 613 1.1 Some useful notation ................................ 614 1.2 Equality. The first axiomatization ......................... 615 1.3 Paramodulation and its refinements ........................ 616 1.4 Equality in sequent systems ..."
Abstract

Cited by 20 (7 self)
 Add to MetaCart
Contents i Introduction ........................................ 613 1.1 Some useful notation ................................ 614 1.2 Equality. The first axiomatization ......................... 615 1.3 Paramodulation and its refinements ........................ 616 1.4 Equality in sequent systems ............................. 622 1.5 Overview of calculi introduced in this chapter ................... 628 2 Translation of logic with equality into logic without equality ............. 628 2.1 Modification method ................................. 630 2.2 Constrained equality elimination .......................... 633 3 Free variable systems ................................... 637 3.1 Free variable tableaux ................................ 637 3.2 Matings ........................................ 640 3.3 The inverse method ................................. 641 4 Early history ........................................ 644 5 Simultaneous rigid Eunification ............................. 646 5
TPS: A TheoremProving System for Classical Type Theory
, 1996
"... . This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
. This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higherorder logic. AMS Subject Classification: 0304, 68T15, 03B35, 03B15, 03B10. Key words: higherorder logic, type theory, mating, connection, expansion proof, natural deduction. 1. Introduction TPS is a theoremproving system for classical type theory ## (Church's typed #calculus [20]) which has been under development at Carnegie Mellon University for a number years. This paper gives a general...
On the axiomatisation of Boolean categories with and without medial, 2005. Preprint, available at http://arxiv.org/abs/cs.LO/0512086
"... Abstract. In its most general meaning, a Boolean category is to categories what a Boolean algebraic structure underlying the proofs in Boolean Logic, in the same sense as a ..."
Abstract

Cited by 15 (8 self)
 Add to MetaCart
Abstract. In its most general meaning, a Boolean category is to categories what a Boolean algebraic structure underlying the proofs in Boolean Logic, in the same sense as a
A Calculus and a System Architecture for Extensional HigherOrder Resolution
, 1997
"... The first part of this paper introduces an extension for a variant of Huet's higherorder resolution calculus [Hue72, Hue73] based upon classical type theory (Church's typed calculus [Chu40]) in order to obtain a calculus which is complete with respect to Henkin models [Hen50]. The new rules connec ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
The first part of this paper introduces an extension for a variant of Huet's higherorder resolution calculus [Hue72, Hue73] based upon classical type theory (Church's typed calculus [Chu40]) in order to obtain a calculus which is complete with respect to Henkin models [Hen50]. The new rules connect higherorder preunification with the general refutation process in an appropriate way to establish full extensionality for the whole system. The general idea of the calculus is discussed on different examples. The second part introduces the Leo system which implements the discussed extensional higherorder resolution calculus. This part mainly focus on the embedding of the new extensionality rules into the refutation process and the treatment of higherorder unification. 1 Introduction Many mathematical problems can be expressed shortly and elegantly in higher order logic whereas they often lead to unnatural and inflated formulations in firstorder logic, e.g., when coding them into axio...
Clause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning
 ARTIFICIAL INTELLIGENCE
"... A new methodology/data structure, the clause tree, is developed for automated reasoning based on resolution in first order logic. A clause tree T on a set S of clauses is a 4tuple , where N is a set of nodes, divided into clause nodes and atom nodes, E is a set of edges, each of which join ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
A new methodology/data structure, the clause tree, is developed for automated reasoning based on resolution in first order logic. A clause tree T on a set S of clauses is a 4tuple <N,E,L,M>, where N is a set of nodes, divided into clause nodes and atom nodes, E is a set of edges, each of which joins a clause node to an atom node, L is a labeling of N E which assigns to each clause node a clause of S, to each atom node an instance of an atom of some clause of S, and to each edge either + or . The edge joining a clause node to an atom node is labeled by the sign of the corresponding literal in the clause. A resolution is represented by unifying two atom nodes of different clause trees which represent complementary literals. The merge of two identical literals is represented by placing the path joining the two corresponding atom nodes into the set M of chosen merge paths. The tail of the merge path becomes a closed leaf, while the head remains an open leaf which can be resolved on. Th...
General Connections via Equality Elimination
 Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI95
, 1995
"... A new way of handling equality in the connection method is described. Our method is called equality elimination. It does not require rigid Eunification which is the basis of most known extension procedures. Equality elimination uses efficient ordering strategies via basic superposition and simplif ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
A new way of handling equality in the connection method is described. Our method is called equality elimination. It does not require rigid Eunification which is the basis of most known extension procedures. Equality elimination uses efficient ordering strategies via basic superposition and simplification. In addition, we present a new treatment of the connection method via named matrices which gives a number of advantages. Section 1 Introduction We propose an approach to adding equality to extension proof methods which are known under two different names connection method [BS 75, Bib 87] and the method of matings [And 76, And 81, Gal 90, Gal 92]. Both methods express the same idea going back to the fundamental Herbrand theorem [Her 30, Min 66, Min 67a]. According to these approaches, the proofsearch can be considered as a the problem of verifying that each path through a matrix of the goal formula is complementary (in the nonequality case it means that each path contains a litera...
Compressing propositional refutations
 Sixth International Workshop on Automated Verification of Critical Systems (AVOCS ’06) – Preliminary Proceedings
, 2006
"... We report initial results on shortening propositional resolution refutation proofs. This has an application in speeding up deductive reconstruction (in theorem provers) of large propositional refutations, such as those produced by SATsolvers. Key words: Proof verification, Propositional refutations ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We report initial results on shortening propositional resolution refutation proofs. This has an application in speeding up deductive reconstruction (in theorem provers) of large propositional refutations, such as those produced by SATsolvers. Key words: Proof verification, Propositional refutations 1