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Rewriting Logic as a Logical and Semantic Framework
, 1993
"... Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are und ..."
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Cited by 147 (52 self)
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Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...
Soft Linear Logic and Polynomial Time
 THEORETICAL COMPUTER SCIENCE
, 2002
"... We present a subsystem of second order Linear Logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms, and viceversa. ..."
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Cited by 48 (0 self)
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We present a subsystem of second order Linear Logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms, and viceversa.
A dialecticalike model of linear logic
 In Proc. Conf. on Category Theory and Computer Science, LNCS 389
, 1989
"... The aim of this work is to define the categories GC, describe their categorical structure and show they are a model of Linear Logic. The second goal is to relate those categories to the Dialectica categories DC, cf.[DCJ, using different functors for the exponential “of course”. It is hoped that this ..."
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Cited by 27 (6 self)
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The aim of this work is to define the categories GC, describe their categorical structure and show they are a model of Linear Logic. The second goal is to relate those categories to the Dialectica categories DC, cf.[DCJ, using different functors for the exponential “of course”. It is hoped that this categorical model of Linear Logic should help us to get a better understanding of the logic, which is, perhaps, the first nonintuitionistic constructive logic. This work is divided in two parts, each one with 3 sections. The first section shows that GC is a monoidal closed category and describes bifunctors for tensor “0”, internal horn “[—, —]“, par “u”, cartesian products “& “ and coproducts “s”. The second section defines linear negation as a contravariant functor obtained evaluating the internal horn bifunctor at a “dualising object”. The third section makes explicit the connections with Linear Logic, while the fourth introduces the comonads used to model the connective “of course”. Section 5 discusses some properties of these cornonads and finally section 6 makes the logical connections once more. This work grew out of suggestions of J.Y. Girard at the AMSConference on Categories, Logic and Computer Science in Boulder 1987, where I presented my earlier work on the Dialectica categories, hence the title. Still on the lines of given credit where it is due, I would like to say that Martin Hyland, under whose supervision this work was written, has been a continuous source of ideas and inspiration. Many heartfelt thanks to him. 1. The main definitions We start with a finitely complete category C. Then to describe GC say that its objects are relations on objects of C, that is monics A ~ U x X, which we usually write as (U ~ X). Given two such objects, (U ~ X) and (V L Y), which we call simply A and B, a morphism from A to B consists of a pair of maps in C, f: U — * V and F 4 Y —+ X, such that a pullback condition is satisfied, namely that where (~~)_1 represents puilbacks. (U x F) 1 (o~) ~ (f x Y) 1 (/3), (1) 342 Using diagrams, we say (f,F) is a morphism in GC if there is a (unique) map in ~, k: A ’ —~B ’ making the triangle commute: a~I Ia
Incremental processing and acceptability
 Computational Linguistics
, 2000
"... We describe a lefttoright incremental procedure for the processing of Lambek categorial grammar by proof net construction. A simple metric of complexity, the profile in time of the number of unresolved valencies, correctly predicts a wide variety of performance phenomena including garden pathing, ..."
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Cited by 26 (4 self)
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We describe a lefttoright incremental procedure for the processing of Lambek categorial grammar by proof net construction. A simple metric of complexity, the profile in time of the number of unresolved valencies, correctly predicts a wide variety of performance phenomena including garden pathing, the unacceptability of center embedding, preference for lower attachment, lefttoright quantifier scope preference, and heavy noun phrase shift.
Grail: A Functional Form for Imperative Mobile Code
, 2003
"... In Robert Louis Stevenson's novel [31], Dr Jekyll is a wellregarded member of polite society, while his alter ego Mr Hyde shares the same physical form but roams abroad communing with the lowest elements. In this paper we present Grail, a wellbehaved firstorder functional language that is the tar ..."
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Cited by 25 (12 self)
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In Robert Louis Stevenson's novel [31], Dr Jekyll is a wellregarded member of polite society, while his alter ego Mr Hyde shares the same physical form but roams abroad communing with the lowest elements. In this paper we present Grail, a wellbehaved firstorder functional language that is the target for an MLlike compiler; while also being a wholly imperative language of assignments that travels and executes as Java classfiles. We use this dual identity in the Mobile Resource Guarantees project, where Grail serves as proofcarrying code to provide assurances of time and space performance, thereby supporting secure and reliable global computing.
Local Possibilistic Logic
 Journal of Applied NonClassical Logic
, 1997
"... Possibilistic states of information are fuzzy sets of possible worlds. They constitute a complete lattice, which can be endowed with a monoidal operation (a tnorm) to produce a quantal. An algebraic semantics is presented which links possibilistic formulae with information states, and gives a natur ..."
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Cited by 21 (14 self)
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Possibilistic states of information are fuzzy sets of possible worlds. They constitute a complete lattice, which can be endowed with a monoidal operation (a tnorm) to produce a quantal. An algebraic semantics is presented which links possibilistic formulae with information states, and gives a natural interpretation of logical connectives as operations on fuzzy sets. Due to the quantal structure of information states, we obtain a system which shares several features with (exponentialfree) intuitionistic linear logic. Soundness and completeness are proved, parametrically on the choice of the tnorm operation.
An algebraic semantics for possibilistic logic
 Uncertainty in Artificial Intelligence (UAI 95
, 1995
"... The first contribution of this paper is the presentation of a Pavelka–like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (¬) and a new type of conjunction (⊗). The space of truth values for this logic is the lattice of poss ..."
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Cited by 15 (9 self)
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The first contribution of this paper is the presentation of a Pavelka–like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (¬) and a new type of conjunction (⊗). The space of truth values for this logic is the lattice of possibility functions, that, from an algebraic point of view, forms a quantal. A second contribution comes from the understanding of the new conjunction as the combination of tokens of information coming from different sources, which makes our language ”dynamic”. A Gentzen calculus is presented, which is proved sound and complete with respect to the given semantics. The problem of truth functionality is discussed in this context. 1
Stratified coherent spaces: a denotational semantics for Light Linear Logic (Extended Abstract)
 Theoretical Computer Science
, 2000
"... We introduce a stratified version of the coherent spaces model where an object is given by a sequence of coherent spaces. The intuition behind it is that each level gives a di#erent degree of precision on the computation, an appearance. A morphism is required to satisfy a coherence condition at each ..."
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Cited by 15 (5 self)
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We introduce a stratified version of the coherent spaces model where an object is given by a sequence of coherent spaces. The intuition behind it is that each level gives a di#erent degree of precision on the computation, an appearance. A morphism is required to satisfy a coherence condition at each level and this setting gives a model of Elementary Linear Logic. We then introduce a measure function on the web meant to describe the di#erence between the number of output and input requests in the computation. The locally bounded morphisms defined thanks to this measure give a subcategory which is a model of Light Linear Logic. 1
Algebra and Sequent Calculus for Epistemic Actions
 ENTCS PROCEEDINGS OF LOGIC AND COMMUNICATION IN MULTIAGENT SYSTEMS (LCMAS) WORKSHOP, ESSLLI 2004
, 2005
"... We introduce an algebraic approach to Dynamic Epistemic Logic. This approach has the advantage that: (i) its semantics is a transparent algebraic object with a minimal set of primitives from which most ingredients of Dynamic Epistemic Logic arise, (ii) it goes with the introduction of nondeterminis ..."
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Cited by 12 (3 self)
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We introduce an algebraic approach to Dynamic Epistemic Logic. This approach has the advantage that: (i) its semantics is a transparent algebraic object with a minimal set of primitives from which most ingredients of Dynamic Epistemic Logic arise, (ii) it goes with the introduction of nondeterminism, (iii) it naturally extends beyond boolean sets of propositions, up to intuitionistic and nondistributive situations, hence allowing to accommodate constructive computational, informationtheoretic as well as nonclassical physical settings, and (iv) introduces a structure on the actions, which now constitute a quantale. We also introduce a corresponding sequent calculus (which extends Lambek calculus), in which propositions, actions as well as agents appear as resources in a resourcesensitive dynamicepistemic logic.