scholarly journals The Undecidability of Boolean BI through Phase Semantics

2010 ◽  
Author(s):  
Dominique Larchey-Wendling ◽  
Didier Galmiche
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
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