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A temporallogic approach to bindingtime analysis
 In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science
, 1996
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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Cited by 81 (5 self)
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
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Cited by 41 (3 self)
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This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
A Computational Interpretation of Modal Proofs
 Proof Theory of Modal Logics
, 1994
"... The usual (e.g. Prawitz's) treatment of natural deduction for modal logics involves a complicated rule for the introduction of the necessity, since the naive one does not allow normalization. We propose natural deduction systems for the positive fragments of the modal logics K, K4, KT, and S4, exten ..."
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Cited by 28 (2 self)
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The usual (e.g. Prawitz's) treatment of natural deduction for modal logics involves a complicated rule for the introduction of the necessity, since the naive one does not allow normalization. We propose natural deduction systems for the positive fragments of the modal logics K, K4, KT, and S4, extending previous work by Masini on a twodimensional generalization of Gentzen's sequents (2sequents). The modal rules closely match the standard rules for an universal quantifier and different logics are obtained with simple conditions on the elimination rule for 2. We give an explicit term calculus corresponding to proofs in these systems and, after defining a notion of reduction on terms, we prove its confluence and strong normalization. 1. Introduction Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent impossibility to obtain elegant, natural systems for intensional operators (with the excellent ex...
Elimination of Negation in a Logical Framework
, 2000
"... Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with ..."
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Cited by 10 (3 self)
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Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higherorder HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.
On Computational Interpretations of the Modal Logic S4 I. Cut Elimination
 Institut fur Logik, Komplexitat und Deduktionssysteme, Universitat
, 1996
"... A language of constructions for minimal logic is the calculus, where cutelimination is encoded as fireduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cutelimination for the corresponding sequent system. It turns o ..."
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Cited by 8 (6 self)
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A language of constructions for minimal logic is the calculus, where cutelimination is encoded as fireduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cutelimination for the corresponding sequent system. It turns out that a natural interpretation of the latter constructions is a calculus extended by an idealized version of Lisp's eval and quote constructs. In this first part, we analyze how cutelimination works in the standard sequent system for minimal S4, and where problems arise. Bierman and De Paiva's proposal is a natural language of constructions for this logic, but their calculus lacks a few rules that are essential to eliminate all cuts. The S4  calculus, namely Bierman and De Paiva's proposal extended with all needed rules, is confluent. There is a polynomialtime algorithm to compute principal typings of given terms, or answer that the given terms are not typable. The typed S4calculus te...
On a Modal \lambdaCalculus for S4*
 Proceedings of the Eleventh Conference on Mathematical Foundations of Programming Sematics
, 1995
"... We present !2 , a concise formulation of a proof term calculus for the intuitionistic modal logic S4 that is wellsuited for practical applications. We show that, with respect to provability, it is equivalent to other formulations in the literature, sketch a simple type checking algorithm, and pr ..."
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Cited by 7 (0 self)
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We present !2 , a concise formulation of a proof term calculus for the intuitionistic modal logic S4 that is wellsuited for practical applications. We show that, with respect to provability, it is equivalent to other formulations in the literature, sketch a simple type checking algorithm, and prove subject reduction and the existence of canonical forms for welltyped terms. Applications include a new formulation of natural deduction for intuitionistic linear logic, modal logical frameworks, and a logical analysis of staged computation and bindingtime analysis for functional languages [6]. 1 Introduction Modal operators familiar from traditional logic have received renewed attention in computer science through their importance in linear logic. Typically, they are described axiomatically in the style of Hilbert or via sequent calculi. However, the CurryHoward isomorphism between proofs and terms is most poignant for natural deduction, so natural deduction formulations of modal and...
Logical Foundations of Eval/Quote Mechanisms, and the Modal Logic S4
 IN PRESS S15708683(05)000431/FLA AID:71 Vol.•••(•••) [DTD5] P.12 (112) JAL:m1a v 1.40 Prn:15/07/2005; 8:08 jal71 by:SL p. 12 12 N. Alechina, D. Shkatov / Journal of Applied Logic
, 1997
"... Starting from the idea that cut elimination is the precise meaning of program execution, we design two languages of constructions for the minimal logic S4, yielding calculi with idealized versions of Lisp's eval and quote. The first, the S4 calculus, is based on Bierman and De Paiva's proposal, ..."
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Cited by 5 (0 self)
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Starting from the idea that cut elimination is the precise meaning of program execution, we design two languages of constructions for the minimal logic S4, yielding calculi with idealized versions of Lisp's eval and quote. The first, the S4 calculus, is based on Bierman and De Paiva's proposal, and has all desirable logical properties, except for its nonoperational flavor. The second, the evQcalculus, is more complicated, but has a clear operational meaning: it is a tower of interpreters in the style of Lisp's reflexive tower. Remarkably, this language was developed from purely logical principles, but nonetheless provides some operational insight into eval/quote mechanisms. 1 Introduction Let's consider two dual questions. The first is: is there a proofsasprograms, formulasas types correspondence for the modal logic S4? There is one between minimal and intuitionistic logics and  calculi [How80], and also for classical logic [Gri90] or linear logic [Abr93], so why not S4? A...
HigherOrder Categorical Grammars
 Proceedings of Categorial Grammars 04
"... into two principal paradigms: modeltheoretic syntax (MTS), which ..."
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Cited by 4 (1 self)
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into two principal paradigms: modeltheoretic syntax (MTS), which
Labeled deduction in the composition of form and meaning
 IN H.J. OHLBACH & U. REYLE (EDS.) LOGIC, LANGUAGE AND REASONING. ESSAYS IN HONOR OF DOV GABBAY, PART I
, 1999
"... In the late Fifties, Jim Lambek has started a line of investigation that accounts for the composition of form and meaning in natural language in deductive terms: formal grammar is presented as a logic — a system for reasoning about the basic form/meaning units of language and the ways they can be pu ..."
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Cited by 2 (0 self)
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In the late Fifties, Jim Lambek has started a line of investigation that accounts for the composition of form and meaning in natural language in deductive terms: formal grammar is presented as a logic — a system for reasoning about the basic form/meaning units of language and the ways they can be put together into wellformed structured configurations. The reception of the categorial grammar logics in linguistic circles has always been somewhat mixed: the mathematical elegance of the original system ([Lambek 58]) is counterbalanced by clear descriptive limitations, as Lambek has been the first to emphasize on a variety of occasions. As a result of the deepened understanding of the options for ‘substructural ’ styles of reasoning, the categorial architecture has been redesigned in recent work, in ways that suggest that mathematical elegance may indeed be compatible with linguistic sophistication. A careful separation of the logical and the structural components of the categorial inference engine leads to the identification of constants of grammatical reasoning. At the level of the basic rules of use and proof for these constants one finds an explanation for the uniformities in the composition of form and meaning across languages. Crosslinguistic variation in the realization of the formmeaning correspondence is captured in terms of structural inference packages, acting as plugins with respect to the base logic of the grammatical