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Axioms and models of linear logic
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]
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
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]
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
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
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]
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]
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
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]
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]
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
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
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]
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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