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Resource Graphs and Countermodels in Resource Logics

Didier Galmiche, Daniel Méry
2005 Electronical Notes in Theoretical Computer Science  
In this abstract we emphasize the role of a semantic structure called resource graph in order to study the provability in some resource-sensitive logics, like the Bunched Implications Logic (BI) or the  ...  in this logic.  ...  A Countermodel in a Latex file generated the resource graph described in section 3.  ... 
doi:10.1016/j.entcs.2004.06.069 fatcat:b3ton3aln5c27kczbelzafclui

The semantics of BI and resource tableaux

D. GALMICHE, D. MÉRY, D. PYM
2005 Mathematical Structures in Computer Science  
We prove soundness and completeness theorems for a resource tableaux method TBI with respect to this semantics and provide a way to build countermodels from so-called dependency graphs.  ...  The logic of bunched implications, BI, provides a logical analysis of a basic notion of resource rich enough, for example, to form the logical basis for "pointer logic" and "separation logic" semantics  ...  We are grateful to Hongseok Yang, Peter O'Hearn, and the anonymous referees for their help with finding errors in, and with the presentation of, this long and complex paper.  ... 
doi:10.1017/s0960129505004858 fatcat:n2gktzqns5d57pq3phcf6mlvcm

Tableaux and Resource Graphs for Separation Logic

D. Galmiche, D. Mery
2009 Journal of Logic and Computation  
We then provide a tableau calculus that allows us to build such resource graphs from which either proofs, or countermodels can be generated.  ...  We first define specific structures, called resource graphs, that capture SLP models by considering heaps as resources via a labelling process.  ...  SL models inside specific structures called resource graphs from which validity, entailment and countermodel contruction in SL can be analyzed.  ... 
doi:10.1093/logcom/exn066 fatcat:qj6lwlbf4fatlgpn6h2w7y6nju

A family of Gödel hybrid logics

Didier Galmiche, Yakoub Salhi
2010 Journal of Applied Logic  
In this paper, we define a family of fuzzy hybrid logics that are based on Gödel logic.  ...  As these rules are strongly invertible the procedures naturally allow one to generate countermodels. Therefore we prove the decidability and the finite model property for these logics.  ...  Let us recall that the search for alternating chains in bi-graphs in the case of Gödel logics can be characterized as a resource use bounding problem in some particular process calculus [21] .  ... 
doi:10.1016/j.jal.2010.08.008 fatcat:vdfll4xjdbf4tbdkni4tst6bwi

Intuitionistic Layered Graph Logic [chapter]

Simon Docherty, David Pym
2016 Lecture Notes in Computer Science  
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature.  ...  Docherty and D. Pym. Intuitionistic Layered Graph Logic. Proc. IJCAR 2016, Coimbra, Portugal. LNAI 9706:469-486, 2016  ...  The logic is sound and complete with respect to a labelled tableaux system that outputs layered graph countermodels for invalid formulae.  ... 
doi:10.1007/978-3-319-40229-1_32 fatcat:ackw5d3w2ras7m3vb7odrv5hiy

Intuitionistic Layered Graph Logic

Simon Docherty, David Pym
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature.  ...  As in other bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications  ...  The logic is sound and complete with respect to a labelled tableaux system that outputs layered graph countermodels for invalid formulae.  ... 
doi:10.24963/ijcai.2017/673 dblp:conf/ijcai/DochertyP17 fatcat:pjvteytgcbaxrmmkpz4ovcyzzi

OUP accepted manuscript

2019 Journal of Logic and Computation  
The logic combines Boolean BI's resource semantics-we introduce BI and its resource semantics at some length-with epistemic agency.  ...  We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents' local resources.  ...  Acknowledgements We are grateful to Simon Docherty and to the anonymous referees for their comments on earlier drafts of this paper.  ... 
doi:10.1093/logcom/exz024 fatcat:uz2oxrh7evhmrm4rb7oze4osmq

Page 562 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
and countermodel generation in propositional BI logic (extended abstract) (263-282); Mizuhito Ogawa, Generation of a linear time query processing algorithm based on well-quasi-orders (283-297); Christine  ...  in distributed computation (64-81); Martin Abadi and Jan Jiirjens, Formal eavesdropping and its computa- tional interpretation (82-94); Kazunori Ueda, Resource-passing concurrent programming (95-126);  ... 

Intuitionistic Layered Graph Logic: Semantics and Proof Theory [article]

Simon Docherty, David Pym
2018 arXiv   pre-print
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature.  ...  We utilise this result in two ways. First, we prove decidability of the logic by showing the finite embeddability property holds for the algebraic semantics.  ...  This construction of a countermodel would fail in the analogous labelled tableaux system for LGL (i.e., the layered graph logic with classical additives [9] ).  ... 
arXiv:1702.05795v3 fatcat:euas2qm3avhlzgfhozrt2z27ie

A Substructural Epistemic Resource Logic: Theory and Modelling Applications [article]

Didier Galmiche, Pierre Kimmel, David Pym
2019 arXiv   pre-print
The logic combines Boolean BI's resource semantics --- we introduce BI and its resource semantics at some length --- with epistemic agency.  ...  We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents' local resources.  ...  Acknowledgements We are grateful to Simon Docherty and to the anonymous referees for their comments on earlier drafts of this paper.  ... 
arXiv:1909.07296v1 fatcat:aksqqhwgn5fbjb3kqyxvw4hyla

Resolution Proofs and Skolem Functions in QBF Evaluation and Applications [chapter]

Valeriy Balabanov, Jie-Hong R. Jiang
2011 Lecture Notes in Computer Science  
Almost all of the Skolem-function models (respectively countermodels) are computable, under resource limits, from the cube-resolution proofs of the true cases (respectively clause-resolution proofs of  ...  Secondly, it practically conceives Skolem-function countermodels for false QBF, and thus yielding a symmetric view between satisfiability and unsatisfiability certifications.  ...  This work was supported in part by the National Science Council under grants NSC 99-2221-E-002-214-MY3 and NSC 99-2923-E-002-005-MY3.  ... 
doi:10.1007/978-3-642-22110-1_12 fatcat:c7kf3ypvajgevo36qm6j7ola6a

Unified QBF certification and its applications

Valeriy Balabanov, Jie-Hong R. Jiang
2012 Formal methods in system design  
This paper identifies the missing Herbrand-function countermodel for false QBF, and strengthens the connection between syntactic and semantic certificates by showing that, given a true QBF, its Skolemfunction  ...  To date the certificate of a true formula can be in the form of either a syntactic cube-resolution proof or a semantic Skolem-function model whereas that of a false formula is only in the form of a syntactic  ...  Acknowledgements The authors are grateful to Roderick Bloem and Georg Hofferek for providing the relation determinization benchmarks.  ... 
doi:10.1007/s10703-012-0152-6 fatcat:52blnevvbvaljc6sls2j3k7wjy

First-order logic for safety verification of hedge rewriting systems

Alexei Lisitsa
2015 Electronic Communications of the EASST  
In this paper we deal with verification of safety properties of hedge rewriting systems and their generalizations.  ...  The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which is further tackled by a generic finite model finding procedure.  ...  The protocol supervises the access to a shared resource of a set of processes arranged in a tree topology. The processes competing for the resource are located in the leaves of the trees.  ... 
doi:10.14279/tuj.eceasst.72.1020 dblp:journals/eceasst/Lisitsa15 fatcat:u6b4weflsbbt5hll3zk3wjekz4

Bounding Resource Consumption with Gödel-Dummett Logics [chapter]

Dominique Larchey-Wendling
2005 Lecture Notes in Computer Science  
In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi.  ...  Gödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models.  ...  Logical syntax for CL and LC In this section we present the syntax we use for logical formulae.  ... 
doi:10.1007/11591191_47 fatcat:ahk5x7d2bzcdxdgzusvzlail4a

A Substructural Epistemic Resource Logic [chapter]

Didier Galmiche, Pierre Kimmel, David Pym
2016 Lecture Notes in Computer Science  
The logic combines Boolean BI's resource semantics with epistemic agency. We give a labelled tableaux calculus and establish soundness and completeness with respect to the resource semantics.  ...  We illustrate the use of the logic by discussing an example of side-channels in access control using resource tokens.  ...  Related analyses, employing logical models of layered graphs, can be found in [5] . We start with a simple model, depicted in Figure 1 , and gradually refine it.  ... 
doi:10.1007/978-3-662-54069-5_9 fatcat:6theufuk6zednmk6tf7yaemdhi
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