Results 1  10
of
7,527
A KripkeJoyal Semantics for Noncommutative Logic in Quantales
"... abstract. A structural semantics is developed for a firstorder logic, with infinite disjunctions and conjunctions, that is characterised algebraically by quantales. The model structures involved combine the “covering systems” approach of KripkeJoyal intuitionistic semantics from topos theory with ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
with the ordered groupoid structures used to model various connectives in substructural logics. The latter are used to interpret the noncommutative quantal conjunction & (“and then”) and its residual implication connectives. The completeness proof uses the MacNeille completion and the theory of quantic nuclei
Linear Logic and Noncommutativity in the Calculus of Structures
, 2003
"... macro \clap,whichisused on almost every page, came out of such a discussion. This thesis would not exist without the support of my wife Jana. During all the time she has been a continuous source of love and inspiration. This PhD thesis has been written with the financial support of the DFGGraduiert ..."
Abstract

Cited by 45 (13 self)
 Add to MetaCart
.................................... 5 1.3Noncommutativity ................................ 8 1.4The Calculus of Structures . .......................... 9 1.5 Summary of Results............................... 12 1.6OverviewofContents.............................. 15 2LinearLogic and the Sequent Calculus 17 2.1Formulaeand Sequents
Hopf Algebras and Models of Noncommutative Logic
, 2000
"... We give a denition of categorical models for noncommutative logic, which we call entropic categories, and constructions thereof by means of partial bimonoids and modules over Hopf algebras. 1 Introduction Noncommutative logic, NL for short, has been introduced by Abrusci and the third author in [ ..."
Abstract
 Add to MetaCart
We give a denition of categorical models for noncommutative logic, which we call entropic categories, and constructions thereof by means of partial bimonoids and modules over Hopf algebras. 1 Introduction Noncommutative logic, NL for short, has been introduced by Abrusci and the third author
Noncommutative logic III: focusing proofs \Lambda
, 2002
"... Abstract It is now wellestablished that the socalled focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for noncommutative logic (NL) which enjoys the f ..."
Abstract
 Add to MetaCart
Abstract It is now wellestablished that the socalled focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for noncommutative logic (NL) which enjoys
Noncommutative logic I : the multiplicative fragment
, 1998
"... INTRODUCTION Unrestricted exchange rules of Girard's linear logic [8] force the commutativity of the multiplicative connectives\Omega (times, conjunction) and & (par, disjunction) , and henceforth the commutativity of all logic. This a priori commutativity is not always desirable  it is ..."
Abstract

Cited by 41 (7 self)
 Add to MetaCart
 it is quite problematic in applications like linguistics or computer science , and actually the desire of a noncommutative logic goes back to the very beginning of LL [9]. Previous works on noncommutativity deal essentially with noncommutative fragments of LL, obtained by removing the exchange rule
Natural Deduction for Intuitionistic NonCommutative Linear Logic
 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99
, 1999
"... We present a system of natural deduction and associated term calculus for intuitionistic noncommutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment. ..."
Abstract

Cited by 36 (16 self)
 Add to MetaCart
We present a system of natural deduction and associated term calculus for intuitionistic noncommutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment.
Quantum Logic and NonCommutative Geometry
, 2004
"... We propose a general scheme for the “logic ” of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*algebras, the noncommutative version of measurable functions, arising as envelope of the ..."
Abstract
 Add to MetaCart
We propose a general scheme for the “logic ” of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*algebras, the noncommutative version of measurable functions, arising as envelope
SUBSTRUCTURAL LOGICS ∗
"... A b s t r a c t. The present paper is concerned with the cut eliminability for some sequent systems of noncommutative substructural logics, i.e. substructural logics without exchange rule. Sequent systems of several extensions of noncommutative logics FL and LBB ′ I, which is sometimes called T → − ..."
Abstract
 Add to MetaCart
A b s t r a c t. The present paper is concerned with the cut eliminability for some sequent systems of noncommutative substructural logics, i.e. substructural logics without exchange rule. Sequent systems of several extensions of noncommutative logics FL and LBB ′ I, which is sometimes called
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
Abstract

Cited by 41 (10 self)
 Add to MetaCart
We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine
Results 1  10
of
7,527