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Axioms and models of linear logic

1990
*
Formal Aspects of Computing
*

Girard's recent system

doi:10.1007/bf01888221
fatcat:ic7vezgsubaiphq7h6ttojjrgy
*of**linear**logic*is presented in a way that avoids the two-level structure*of*formulae*and*sequents,*and*that minimises the number*of*primitive function symbols. ... The axiomatisation leads to a complete class*of*algebraic*models*. Various*models*are exhibited. On the meta-level we use Dijkstra's method*of*explicit equational proofs. ... Monoidal*Models**of**Linear**Logic*3.0. In this section, we present a general class*of**models**of**linear**logic*. ...##
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Logic of predicates with explicit substitutions
[chapter]

1996
*
Lecture Notes in Computer Science
*

We present a non-commutative

doi:10.1007/3-540-61550-4_148
fatcat:7srloqu57vdvzhn3qcllmwck2y
*linear**logic*| the*logic**of*predicates with equality*and*explicit substitutions. ... explanation*of*the position*of*usual*logic*with respect to the*linear*. ... Acknowledgements I would like to acknowledge stimulating discussions with colleagues at ICS PAS,*and*in particular I would like to thank Beata Konikowska*and*Andrzej Tarlecki. ...##
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Some Thoughts on Logic and Intuition in Science and Chemical Engineering

2014
*
OALib
*

The intuition-judgments (

doi:10.4236/oalib.1100908
fatcat:bm3gsz7kqfcetnvzob2x6cnt2m
*axioms*)*of*the*linear**and*nonlinear mass transfer theories are presented too. ... The role*of*the*logic**and*intuition in the chemical engineering is presented. ... Conclusion Some thoughts concerning the role*of**logic**and*the intuition in the chemical engineering allow formulating clearly their position in the modern science*and*practices. ...##
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Possibilistic logic as interpretability logic
[chapter]

1995
*
Lecture Notes in Computer Science
*

This contributes to our knowledge on the relations

doi:10.1007/bfb0035960
fatcat:tx2h2kypjrhqbiqy6fb6vrtsuq
*of**logics**of*uncertainty to classical systems*of*modal*logic*. ... It is shown that a variant*of*qualitative (comparative) possibilistic*logic*is closely related to modal interpretability*logic*, as studied in the metamathematics*of*rst-order arithmetic. ... We s h o w that our present tense*logic*is completely axiomatized by an*axiom*system extending the*axioms**of*provability l o g i c L by a single*axiom**of**linear*preorder: Let (E) be the*axiom*2(2A ! ...##
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Axiomatizations for Temporal Epistemic Logic with Perfect Recall over Linear Time

2009
*
2009 16th International Symposium on Temporal Representation and Reasoning
*

We allow both past

doi:10.1109/time.2009.18
dblp:conf/time/MikulasRF09
fatcat:z6njc4epjjhrtpeuhsakebuauq
*and*future operators*and*examine the interpretation*of*different*linear*flows*of*time. ... In particular, we present temporal epistemic*logics*for each*of*the following flows*of*time: arbitrary*linear*orders; the integers; the rationals; the reals;*and*for uniform flows*of*time. ... Besides the*axioms*for propositional*logic*, we have the •*axioms*for epistemic*logic*(stating that every K i is an S5 modality) •*axioms*for*linear*temporal*logic*(for strict F*and*P) (see for example ...##
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Toposes are symmetric monoidal closed categories

2012
*
Scientific Research of the Institute of Mathematics and Computer Science
*

The category theory provides possibilities to

doi:10.17512/jamcm.2012.1.11
fatcat:xxqcxs5g3fctjcvr3vvrst4vti
*model*many important features*of*computer science. We used the symmetric monoidal closed category for the construction*of*a*model**of**linear*type theory. ... This fact will allow us to use topos in the role*of*symmetric monoidal closed category -for construction*of*the*models**of*the type theory. ... In [4] we constructed the*model**of*first-order*linear**logic**and**model**of*the higher-order*linear**logic*without exponentials in toposes. We showed a simpler way to construct those*models*. ...##
###
The Complexity of Non-Iterated Probabilistic Justification Logic
[chapter]

2016
*
Lecture Notes in Computer Science
*

In this paper we establish upper

doi:10.1007/978-3-319-30024-5_16
fatcat:27toicnyrvfyvcprddonc5nxim
*and*lower bounds for the complexity*of*the derivability problem in the*logic*PJ. ... The main result*of*the paper is that the complex- ity*of*the derivability problem in PJ remains the same as the complexity*of*the derivability problem in the underlying*logic*J, which is Πp2-complete. ... Acknowledgements: The author is grateful to Antonis Achilleos*and*the anonymous referees for many useful comments*and*to ERC for financial support (project EPS 313360). ...##
###
Classical Linear Logic of Implications
[chapter]

2002
*
Lecture Notes in Computer Science
*

We give a simple term calculus for the multiplicative exponential fragment

doi:10.1007/3-540-45793-3_31
fatcat:7iuphna6mndvpdomudjssia6x4
*of*Classical*Linear**Logic*, by extending Barber*and*Plotkin's system for the intuitionistic case. ... Despite this simplicity, the calculus is shown to be sound*and*complete for category-theoretic*models*given by * -autonomous categories with*linear*exponential comonads. ... It can be regarded as an extension*of*the Dual Intuitionistic*Linear**Logic*(DILL)*of*Barber*and*Plotkin [1, 2] . ...##
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Classical linear logic of implications

2005
*
Mathematical Structures in Computer Science
*

We give a simple term calculus for the multiplicative exponential fragment

doi:10.1017/s0960129504004621
fatcat:3eb5pyvykbg75ntfgfbpafkd7e
*of*Classical*Linear**Logic*, by extending Barber*and*Plotkin's system for the intuitionistic case. ... Despite this simplicity, the calculus is shown to be sound*and*complete for category-theoretic*models*given by * -autonomous categories with*linear*exponential comonads. ... It can be regarded as an extension*of*the Dual Intuitionistic*Linear**Logic*(DILL)*of*Barber*and*Plotkin [1, 2] . ...##
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The Complexity of Probabilistic Justification Logic
[article]

2017
*
arXiv
*
pre-print

Probabilistic justification

arXiv:1708.04100v1
fatcat:qyvmy4h2nffine5q35wafobxai
*logic*is a modal*logic*with two kind*of*modalities: probability measures*and*explicit justification terms. ... We present a tableau procedure that can be used to decide the satisfiability problem for this*logic*in polynomial space. We show that this upper complexity bound is tight. ... Acknowledgements: The author is grateful to Antonis Achilleos*and*the anonymous referees for many useful comments*and*to ERC for financial support (project EPS 313360). ...##
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Linear models and set theory
[chapter]

2019
*
Seminário Lógica no Avião
*

We then present several paraconsistent set theories based on

doi:10.21452/lna_serie_n_v01_book_seminario-logica-no-aviao-2013-2018_martinez-venturi_p.09-21
fatcat:yj3d27tfe5ejxkqyggegka5e2m
*Logics**of*Formal Inconsistency (LFI), known in the literature as LFI-set theories,*and*we show that there is no natural*model*that validates ... In this paper we review the approach to algebra-valued*models**and*we introduce an infinite class*of*natural*models*for paraconsistent set theory. ... By a paraconsistent*linear**model*we mean a V-*model**of*the form V L , with |L| ą 2,*and*we refer to it as a V˚-*model*. ...##
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Subminimal negation

2016
*
Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

Finally, as a bridge to the work

doi:10.1007/s00500-016-2391-8
fatcat:mlqh4ktzsjdxxi5k3f3ga3r4fe
*of*Franco Montagna a start is made*of*a study*of**linear**models**of*these*logics*. Dedicated to the memory*of*Franco Montagna ... A Kripke semantics is developed for minimal*logic**and*its sublogics with a still weaker negation by introducing a function on the upward closed sets*of*the*models*. ...*models**of*modal*logic*[2, 7] ). ...##
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Formalization of Linear Space Theory in the Higher-Order Logic Proving System

2013
*
Journal of Applied Mathematics
*

Higher-order

doi:10.1155/2013/218492
fatcat:4kjrlnyxlfb4zeh3gxe6wlygqy
*logic*is a form*of*predicate*logic*that is distinguished from first-order*logic*by additional quantifiers*and*stronger semantics. Higher-order*logic*is more expressive. ... This paper presents the formalization*of*the*linear*space theory in HOL4. A set*of*properties is characterized in HOL4. ... Acknowledgment This research was supported by an international scientific*and*technological cooperation project (2011DFG13000) backed by The Ministry*of*Science*and*Technology*of*China. ...##
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PX: A computational logic

1990
*
Discrete Applied Mathematics
*

The concept

doi:10.1016/0166-218x(90)90121-r
fatcat:oqnkcu4qovddnfzwh4nvwc4wxy
*of*block codes. Review*of*the concepts introduced. Chapter 2:*Linear*Codes. Basic concepts. Minimum Hamming distance*of*a code*and*the error detection/correction capability*of*the code. ... The parity matrix*of*a*linear*code. Constructing a general Hamming code. ...*Axioms**of*Join*and*Product. Graph*and*value class: the minimal graph*axiom*). Choice rule. Remarks on the*axiom*system (The*logic**of*partial terms versus the*logic**of*partial existence. ...##
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Deductive plan generation
[chapter]

1994
*
Lecture Notes in Computer Science
*

Understanding

doi:10.1007/3-540-58520-6_47
fatcat:fqq54pj74zeutpcezyxprso2cu
*and**modeling*the ability*of*humans to reason about actions, change,*and*causality is one*of*the key issues in Artificial Intelligence*and*Cognitive Science. ... Kowalski reduced the number*of*frame*axioms*to become*linear*with respect to the number*of*different actions [17] . Some years later, it was again J. ... A third deductive planning method which*models*the concept*of*resources is based on*linear**logic*, which is a Gentzen-style proof system without weakening*and*contraction rules [9] . ...
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