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Axioms and models of linear logic

Wim H. Hesselink
1990 Formal Aspects of Computing  
Girard's recent system 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.  ... 
doi:10.1007/bf01888221 fatcat:ic7vezgsubaiphq7h6ttojjrgy

Logic of predicates with explicit substitutions [chapter]

Marek A. Bednarczyk
1996 Lecture Notes in Computer Science  
We present a non-commutative 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.  ... 
doi:10.1007/3-540-61550-4_148 fatcat:7srloqu57vdvzhn3qcllmwck2y

Some Thoughts on Logic and Intuition in Science and Chemical Engineering

Christo Boyadjiev
2014 OALib  
The intuition-judgments (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.  ... 
doi:10.4236/oalib.1100908 fatcat:bm3gsz7kqfcetnvzob2x6cnt2m

Possibilistic logic as interpretability logic [chapter]

Petr Hájek
1995 Lecture Notes in Computer Science  
This contributes to our knowledge on the relations 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 !  ... 
doi:10.1007/bfb0035960 fatcat:tx2h2kypjrhqbiqy6fb6vrtsuq

Axiomatizations for Temporal Epistemic Logic with Perfect Recall over Linear Time

Szabolcs Mikulas, Mark Reynolds, Tim French
2009 2009 16th International Symposium on Temporal Representation and Reasoning  
We allow both past 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  ... 
doi:10.1109/time.2009.18 dblp:conf/time/MikulasRF09 fatcat:z6njc4epjjhrtpeuhsakebuauq

Toposes are symmetric monoidal closed categories

Viliam Slodičak
2012 Scientific Research of the Institute of Mathematics and Computer Science  
The category theory provides possibilities to 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.  ... 
doi:10.17512/jamcm.2012.1.11 fatcat:xxqcxs5g3fctjcvr3vvrst4vti

The Complexity of Non-Iterated Probabilistic Justification Logic [chapter]

Ioannis Kokkinis
2016 Lecture Notes in Computer Science  
In this paper we establish upper 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).  ... 
doi:10.1007/978-3-319-30024-5_16 fatcat:27toicnyrvfyvcprddonc5nxim

Classical Linear Logic of Implications [chapter]

Masahito Hasegawa
2002 Lecture Notes in Computer Science  
We give a simple term calculus for the multiplicative exponential fragment 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] .  ... 
doi:10.1007/3-540-45793-3_31 fatcat:7iuphna6mndvpdomudjssia6x4

Classical linear logic of implications

MASAHITO HASEGAWA
2005 Mathematical Structures in Computer Science  
We give a simple term calculus for the multiplicative exponential fragment 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] .  ... 
doi:10.1017/s0960129504004621 fatcat:3eb5pyvykbg75ntfgfbpafkd7e

The Complexity of Probabilistic Justification Logic [article]

Ioannis Kokkinis
2017 arXiv   pre-print
Probabilistic justification 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).  ... 
arXiv:1708.04100v1 fatcat:qyvmy4h2nffine5q35wafobxai

Linear models and set theory [chapter]

Santiago Jockwich Martinez, Giorgio Venturi
2019 Seminário Lógica no Avião  
We then present several paraconsistent set theories based on 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.  ... 
doi:10.21452/lna_serie_n_v01_book_seminario-logica-no-aviao-2013-2018_martinez-venturi_p.09-21 fatcat:yj3d27tfe5ejxkqyggegka5e2m

Subminimal negation

Almudena Colacito, Dick de Jongh, Ana Lucia Vargas
2016 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
Finally, as a bridge to the work 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] ).  ... 
doi:10.1007/s00500-016-2391-8 fatcat:mlqh4ktzsjdxxi5k3f3ga3r4fe

Formalization of Linear Space Theory in the Higher-Order Logic Proving System

Jie Zhang, Danwen Mao, Yong Guan
2013 Journal of Applied Mathematics  
Higher-order 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.  ... 
doi:10.1155/2013/218492 fatcat:4kjrlnyxlfb4zeh3gxe6wlygqy

PX: A computational logic

1990 Discrete Applied Mathematics  
The concept 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.  ... 
doi:10.1016/0166-218x(90)90121-r fatcat:oqnkcu4qovddnfzwh4nvwc4wxy

Deductive plan generation [chapter]

Wolfgang Bibel, Michael Thielscher
1994 Lecture Notes in Computer Science  
Understanding 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] .  ... 
doi:10.1007/3-540-58520-6_47 fatcat:fqq54pj74zeutpcezyxprso2cu
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