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Logic Programming with Focusing Proofs in Linear Logic
 Journal of Logic and Computation
, 1992
"... The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is C ..."
Focused Proof Search for Linear Logic in the Calculus of Structures
 in "Technical Communications of the 26th International Conference on Logic Programming (ICLP
, 2010
"... Abstract. The prooftheoretic approach to logic programming has benefited from the introduction of focused proof systems, through the nondeterminism reduction and control they provide when searching for proofs in the sequent calculus. However, this technique was not available in the calculus of str ..."
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Cited by 2 (1 self)
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Abstract. The prooftheoretic approach to logic programming has benefited from the introduction of focused proof systems, through the nondeterminism reduction and control they provide when searching for proofs in the sequent calculus. However, this technique was not available in the calculus
A unified sequent calculus for focused proofs
 In LICS: 24th Symp. on Logic in Computer Science
, 2009
"... Abstract—We present a compact sequent calculus LKU for classical logic organized around the concept of polarization. Focused sequent calculi for classical logic, intuitionistic logic, and multiplicativeadditive linear logic are derived as fragments of LKU by increasing the sensitivity of specialize ..."
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Cited by 16 (7 self)
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. KeywordsProof theory; focused proof systems; linear logic I.
From proofs to focused proofs : a modular proof of focalization in linear logic
 CSL’07, volume 4646 of LNCS
, 2007
"... dale.miller at inria.fr saurin at lix.polytechnique.fr Abstract. Probably the most significant result concerning cutfree sequent calculus proofs in linear logic is the completeness of focused proofs. This completeness theorem has a number of proof theoretic applications — e.g. in games semantics, ..."
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Cited by 26 (9 self)
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dale.miller at inria.fr saurin at lix.polytechnique.fr Abstract. Probably the most significant result concerning cutfree sequent calculus proofs in linear logic is the completeness of focused proofs. This completeness theorem has a number of proof theoretic applications — e.g. in games semantics
Noncommutative logic III: focusing proofs
 Information and Computation
, 2000
"... We present a sequent calculus for noncommutative logic which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permut ..."
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Cited by 5 (2 self)
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We present a sequent calculus for noncommutative logic which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permutabilities of rules for NL and showing that all LL permutabilities involved in focalization can be lifted to NL permutabilities. These results are based on a study of the partitions of partially ordered sets modulo entropy. 1 Introduction Noncommutative logic, NL for short, was introduced by Abrusci and the second author in [1, 15] (see also section 3). It unies commutative linear logic [6] and cyclic linear logic [16], a classical conservative extension of the Lambek calculus [10]. The present paper investigates the \focalization" property for noncommutative logic. 1.1 The property of focalization Rules of the sequent calculus for linear logic [6] are wellknown to split into two c...
Noncommutative logic III: focusing proofs \Lambda
, 2002
"... Abstract It is now wellestablished that the socalled focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for noncommutative logic (NL) which enjoys the f ..."
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Abstract It is now wellestablished that the socalled focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for noncommutative logic (NL) which enjoys
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 795 (42 self)
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of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence
A MultiFocused Proof System Isomorphic to Expansion Proofs
, 2013
"... 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 ..."
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Cited by 1 (0 self)
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proofs. We show that, among the multifocused proofs, the maximally multifocused proofs that collect together all possible parallel foci are canonical. Moreover, if we start with a certain focused sequent proof system, such proofs are isomorphic to expansion proofs—a well known, minimalistic
Active Perception
, 1988
"... Active Perception (Active Vision specifically) is defined as a study of Modeling and Control strategies for perception. By modeling we mean models of sensors, processing modules and their interaction. We distinguish local models from global models by their extent of application in space and time. T ..."
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Cited by 431 (12 self)
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are formulated as a search of such sequence of steps that would minimize a loss function while one is seeking the most information. Examples are shown as the existence proof of the proposed theory on obtaining range from focus and sterolvergence on 2D segmentation of an image and 30 shape parametrization.
Defunctionalizing Focusing Proofs (Or, How Twelf Learned To Stop Worrying And Love The Ωrule)
"... Abstract. In previous work, the author gave a higherorder analysis of focusing proofs (in the sense of Andreoli’s search strategy), with a role for infinitary rules very similar in structure to Buchholz’s Ωrule. Among other benefits, this “patternbased ” description of focusing simplifies the cut ..."
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Abstract. In previous work, the author gave a higherorder analysis of focusing proofs (in the sense of Andreoli’s search strategy), with a role for infinitary rules very similar in structure to Buchholz’s Ωrule. Among other benefits, this “patternbased ” description of focusing simplifies
Results 1  10
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3,614