Results 1  10
of
1,203
Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
Abstract

Cited by 428 (122 self)
 Add to MetaCart
with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cutfree sequent proofs called uniform proofs. A uniform proof is one that can be found by a goaldirected search
Modal Interpolation via Nested Sequents
"... Abstract The main method of proving the Craig Interpolation Property (CIP) constructively uses cutfree sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequentlike proof formalisms, such as hypersequents, nested sequents, and labelled ..."
Abstract
 Add to MetaCart
Abstract The main method of proving the Craig Interpolation Property (CIP) constructively uses cutfree sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequentlike proof formalisms, such as hypersequents, nested sequents
The admissibility of cut in the cutfree sequent calculus
, 2012
"... In the last lecture we saw cut elimination as the global version of cut reduction. In this lecture we begin with identity, which is the global version of identity expansion. Together, they provide the basis for understanding the left and right rules in the sequent calculus as meaning explanations of ..."
Abstract
 Add to MetaCart
of the logical connectives, a program with a long history [Dum91, ML83]. The cutfree sequent calculus is a good basis for proof search, but it still has too much nondeterminism. One way to reduce this nondeterminism is inversion, which we discuss in this lecture. Another is chaining, which will be subject
Completeness of CutFree Sequent Calculus Modulo
"... Abstract. Deduction modulo is a powerful way to replace axioms by rewrite rules and allows to integrate computation in deduction. But adding rewrite rules is not always safe for properties of the deduction system such as consistency or cut elimination. Proving completeness of the cutfree calculus w ..."
Abstract
 Add to MetaCart
Abstract. Deduction modulo is a powerful way to replace axioms by rewrite rules and allows to integrate computation in deduction. But adding rewrite rules is not always safe for properties of the deduction system such as consistency or cut elimination. Proving completeness of the cutfree calculus
Algorithmic Structuring of Cutfree Proofs
 Computer Science Logic. Selected Papers from CSL'92, LNCS 702
, 1993
"... . The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB (LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introducti ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
. The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB (LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides
An Overview of Linear Logic Programming
 in Computational Logic
, 1985
"... Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequen ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer
The Isomorphism Between Expansion Proofs and MultiFocused Sequent Proofs
, 2012
"... The sequent calculus is often criticized for requiring proofs to contain large amounts of lowlevel syntactic details that can obscure the essence of a given proof. Because each inference rule introduces only a single connective, sequent proofs can separate closely related steps—such as instantiatin ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
, instead, an evolutionary approach to recover canonicity within the sequent calculus, which we illustrate for classical firstorder logic. The essential element of our approach is the use of a multifocused sequent calculus as the means for abstracting away lowlevel details from classical cutfree sequent
A CutFree and InvariantFree Sequent Calculus for PLTL ⋆
"... Abstract. Sequent calculi usually provide a general deductive setting that uniformly embeds other prooftheoretical approaches, such as tableaux methods, resolution techniques, goaldirected proofs, etc. Unfortunately, in temporal logic, existing sequent calculi make use of a kind of inference rules ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
, propositional linear temporal logic (PLTL). In this paper, we provide a complete finitary sequent calculus for PLTL, called FC, that not only is cutfree but also invariantfree. In particular, we introduce new rules which provide a new style of temporal deduction. We give a detailed proof of completeness. 1
Forum: A multipleconclusion specification logic
 Theoretical Computer Science
, 1996
"... The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder program ..."
Abstract

Cited by 96 (12 self)
 Add to MetaCart
The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higher
On the proof complexity of cutfree bounded deep inference
, 2011
"... It has recently been shown that cutfree deep inference systems exhibit an exponential speedup over cutfree sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search nondeterminism induced by the deep inference meth ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
It has recently been shown that cutfree deep inference systems exhibit an exponential speedup over cutfree sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search nondeterminism induced by the deep inference
Results 1  10
of
1,203