Phase semantics and verification of concurrent constraint programs

2002 ◽  
Author(s):  
F. Fages ◽  
P. Ruet ◽  
S. Soliman
Keyword(s):  
Phase Semantics

scholarly journals On phase semantics and denotational semantics: the exponentials

2001 ◽  
Vol 109 (3) ◽  
pp. 205-241 ◽  
Author(s):  
Antonio Bucciarelli ◽  
Thomas Ehrhard
Keyword(s):  
Denotational Semantics ◽  
Phase Semantics

scholarly journals Phase semantics and decidability of elementary affine logic

2004 ◽  
Vol 318 (3) ◽  
pp. 409-433 ◽  
Author(s):  
Ugo Dal Lago ◽  
Simone Martini
Keyword(s):  
Phase Semantics

scholarly journals Phase semantics for light linear logic

2003 ◽  
Vol 294 (3) ◽  
pp. 525-549 ◽  
Author(s):  
Max I Kanovich ◽  
Mitsuhiro Okada ◽  
Andre Scedrov
Keyword(s):  
Linear Logic ◽  
Phase Semantics

scholarly journals Nondeterministic Phase Semantics and the Undecidability of Boolean BI

2013 ◽  
Vol 14 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Dominique Larchey-Wendling ◽  
Didier Galmiche
Keyword(s):  
Phase Semantics

scholarly journals Phase Semantics for Light Linear Logic (Extended Abstract)

1997 ◽  
Vol 6 ◽  
pp. 221-234 ◽  
Author(s):  
Max I. Kanovich ◽  
Mitsuhiro Okada ◽  
Andre Scedrov
Keyword(s):  
Linear Logic ◽  
Phase Semantics

scholarly journals Linear Concurrent Constraint Programming: Operational and Phase Semantics

2001 ◽  
Vol 165 (1) ◽  
pp. 14-41 ◽  
Author(s):  
François Fages ◽  
Paul Ruet ◽  
Sylvain Soliman
Keyword(s):  
Constraint Programming ◽  
Phase Semantics ◽  
Concurrent Constraint Programming

Quantales and (noncommutative) linear logic

1990 ◽  
Vol 55 (1) ◽  
pp. 41-64 ◽  
Author(s):  
David N. Yetter
Keyword(s):  
Quantum Mechanics ◽  
Linear Logic ◽  
Physical Experiment ◽  
Quantum Logics ◽  
Von Neumann ◽  
Logical Validity ◽  
Empirical Verification ◽  
Mcgill University ◽  
Phase Semantics ◽  
Element Free

It is the purpose of this paper to make explicit the connection between J.-Y. Girard's “linear logic” [4], and certain models for the logic of quantum mechanics, namely Mulvey's “quantales” [9]. This will be done not only in the case of commutative linear logic, but also in the case of a version of noncommutative linear logic suggested, but not fully formalized, by Girard in lectures given at McGill University in the fall of 1987 [5], and which for reasons which will become clear later we call “cyclic linear logic”.For many of our results on quantales, we rely on the work of Niefield and Rosenthal [10].The reader should note that by “the logic of quantum mechanics” we do not mean the lattice theoretic “quantum logics” of Birkhoff and von Neumann [1], but rather a logic involving an associative (in general noncommutative) operation “and then”. Logical validity is intended to embody empirical verification (whether a physical experiment, or running a program), and the validity of A & B (in Mulvey's notation) is to be regarded as “we have verified A, and then we have verified B”. (See M. D. Srinivas [11] for another exposition of this idea.)This of course is precisely the view of the “multiplicative conjunction”, ⊗, in the phase semantics for Girard's linear logic [4], [5]. Indeed the quantale semantics for linear logic may be regarded as an element-free version of the phase semantics.

Non-commutative logic II: sequent calculus and phase semantics

2000 ◽  
Vol 10 (2) ◽  
pp. 277-312 ◽  
Author(s):  
PAUL RUET
Keyword(s):  
Special Class ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Partial Orders ◽  
Cut Elimination ◽  
Phase Semantics ◽  
Entropy Relation

Non-commutative logic, which is a unification of commutative linear logic and cyclic linear logic, is extended to all linear connectives: additives, exponentials and constants. We give two equivalent versions of the sequent calculus (directly with the structure of order varieties, and with their presentations as partial orders), phase semantics and a cut-elimination theorem. This involves, in particular, the study of the entropy relation between partial orders, and the introduction of a special class of order varieties: the series–parallel order varieties.

Phase semantics for linear-time formalism

2010 ◽  
Vol 19 (1) ◽  
pp. 121-143 ◽  
Author(s):  
N. Kamide
Keyword(s):  
Linear Time ◽  
Time Formalism ◽  
Phase Semantics

On the unification of classical, intuitionistic and affine logics

2018 ◽  
Vol 29 (8) ◽  
pp. 1177-1216
Author(s):  
CHUCK LIANG
Keyword(s):  
Intuitionistic Logic ◽  
Classical Logic ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Kripke Semantics ◽  
Cut Elimination ◽  
Structural Rules ◽  
Phase Semantics ◽  
Intuitionistic Logics

This article presents a unified logic that combines classical logic, intuitionistic logic and affine linear logic (restricting contraction but not weakening). We show that this unification can be achieved semantically, syntactically and in the computational interpretation of proofs. It extends our previous work in combining classical and intuitionistic logics. Compared to linear logic, classical fragments of proofs are better isolated from non-classical fragments. We define a phase semantics for this logic that naturally extends the Kripke semantics of intuitionistic logic. We present a sequent calculus with novel structural rules, which entail a more elaborate procedure for cut elimination. Computationally, this system allows affine-linear interpretations of proofs to be combined with classical interpretations, such as the λμ calculus. We show how cut elimination must respect the boundaries between classical and non-classical modes of proof that correspond to delimited control effects.

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