Results 1  10
of
76
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 ..."
Abstract

Cited by 163 (55 self)
 Add to MetaCart
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. ..."
Abstract

Cited by 69 (0 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 32 (6 self)
 Add to MetaCart
(Show Context)
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, ..."
Abstract

Cited by 27 (4 self)
 Add to MetaCart
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 th ..."
Abstract

Cited by 27 (13 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 22 (14 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
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
A convenient differential category
, 2011
"... We show that the category of convenient vector spaces in the sense of Frölicher ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
We show that the category of convenient vector spaces in the sense of Frölicher
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 ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
(Show Context)
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.