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19
A Modal Deconstruction of Access Control Logics
"... Abstract. We present a translation from a logic of access control with a “says ” operator to the classical modal logic S4. We prove that the translation is sound and complete. We also show that it extends to logics with boolean combinations of principals and with a “speaks for ” relation. While a st ..."
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Cited by 29 (8 self)
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Abstract. We present a translation from a logic of access control with a “says ” operator to the classical modal logic S4. We prove that the translation is sound and complete. We also show that it extends to logics with boolean combinations of principals and with a “speaks for ” relation. While a straightforward definition of this relation requires secondorder quantifiers, we use our translation for obtaining alternative, quantifierfree presentations. We also derive decidability and complexity results for the logics of access control. 1
Proof search in an authorization logic
, 2009
"... We consider the problem of proof search in an expressive authorization logic that contains a “says ” modality and an ordering on principals. After a description of the proof system for the logic, we identify two fragments that admit complete goaldirected and saturating proof search strategies. A sm ..."
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Cited by 9 (5 self)
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We consider the problem of proof search in an expressive authorization logic that contains a “says ” modality and an ordering on principals. After a description of the proof system for the logic, we identify two fragments that admit complete goaldirected and saturating proof search strategies. A smaller fragment is then presented, which supports both goaldirected and saturating search, and has a sound and complete translation to firstorder logic. We conclude with a brief description of our implementation of goaldirected search. This work was supported partially by the iCAST project sponsored by the National Science Council,
Dependent type theory of stateful higherorder functions
, 2005
"... In this paper we investigate a logic for reasoning about programs with higherorder functions and effectful features like nontermination and state with aliasing. We propose a dependent type theory HTT (short for Hoare Type Theory), where types serve as program specifications. In case of effectful p ..."
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Cited by 7 (2 self)
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In this paper we investigate a logic for reasoning about programs with higherorder functions and effectful features like nontermination and state with aliasing. We propose a dependent type theory HTT (short for Hoare Type Theory), where types serve as program specifications. In case of effectful programs, the type of Hoare triples {P}x:A{Q} specifies the precondition P, the type of the return result A, and the postcondition Q. By CurryHoward isomorphism, a dependent type theory may be viewed as a functional programming language. From this perspective, the type of Hoare triples is a monad, and HTT is a monadic language, whose pure fragment consists of higherorder functions, while the effectful fragment is a full Turingcomplete imperative language with conditionals, loops, recursion and commands for stateful operations like allocation, lookup and mutation of location content. 1
Constructive CK for Contexts
 In Proceedings of the First Workshop on Context Representation and Reasoning, CONTEXT’05
, 2005
"... Abstract. This note describes possible world semantics for a constructive modal logic CK. The system CK is weaker than other constructive modal logics K as it does not satisfy distribution of possibility over disjunctions, neither binary (✸(A ∨ B) → ✸A ∨ ✸B) nor nullary (✸ ⊥ → ⊥). We are intereste ..."
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Cited by 5 (2 self)
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Abstract. This note describes possible world semantics for a constructive modal logic CK. The system CK is weaker than other constructive modal logics K as it does not satisfy distribution of possibility over disjunctions, neither binary (✸(A ∨ B) → ✸A ∨ ✸B) nor nullary (✸ ⊥ → ⊥). We are interested in this version of constructive K for its application to contexts in AI [dP03]. However, our previous work on CK described only a categorical semantics [BdPR01] for the system, while most logicians interested in contexts prefer their semantics possible worlds style. This note fills the gap by providing the possible worlds model theory for the constructive modal system CK, showing soundness and completeness of the proposed semantics, as well as the finite model property and (hence) decidability of the system. Wijesekera [Wij90] investigated possible worlds semantics of a system similar to CK, without the binary distribution, but satisfying the nullary one. The semantics presented here for CK is new and considerably simpler than the one of Wijesekera. 1
PrincipalCentric Reasoning in Constructive Authorization Logic
, 2008
"... We present an authorization logic DTL0 that explicitly relativizes reasoning to beliefs of principals. The logic assumes that principals are conceited in their beliefs. We describe the natural deduction system, sequent calculus, Hilbertstyle axiomatization, and Kripke semantics of the logic. We pro ..."
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Cited by 5 (2 self)
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We present an authorization logic DTL0 that explicitly relativizes reasoning to beliefs of principals. The logic assumes that principals are conceited in their beliefs. We describe the natural deduction system, sequent calculus, Hilbertstyle axiomatization, and Kripke semantics of the logic. We prove several metatheoretic results including cutelimination, and soundness and completeness for the Kripke semantics. We also present translations from several other authorization logics into DTL0, and describe formal connections between DTL0 and the modal logic constructive S4.
A Categorical Outlook on Relational Modalities and Simulations
, 2002
"... We characterise bicategories of spans, relations and partial maps universally in terms of factorisations involving maps . We apply this characterisation to show that the standard modalities 2 and arise canonically as the extension of a predicate logic from functions to (abstract) relations . ..."
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Cited by 3 (1 self)
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We characterise bicategories of spans, relations and partial maps universally in terms of factorisations involving maps . We apply this characterisation to show that the standard modalities 2 and arise canonically as the extension of a predicate logic from functions to (abstract) relations .
Contextual Model Type Theory
, 2005
"... this paper we investigate the consequences of relativizing these concepts to explicitly specified contexts. We obtain contextual modal logic and its typetheoretic analogue. Contextual modal type theory provides an elegant, uniform foundation for understanding metavariables and explicit substitutio ..."
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Cited by 3 (0 self)
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this paper we investigate the consequences of relativizing these concepts to explicitly specified contexts. We obtain contextual modal logic and its typetheoretic analogue. Contextual modal type theory provides an elegant, uniform foundation for understanding metavariables and explicit substitutions. We sketch some applications in functional programming and logical frameworks
Bidirectional Decision Procedures for the Intuitionistic Propositional Modal Logic IS4
"... Abstract. We present a multicontext focused sequent calculus whose derivations are in bijective correspondence with normal natural deductions in the propositional fragment of the intuitionistic modal logic IS4. This calculus, suitable for the enumeration of normal proofs, is the starting point for ..."
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Cited by 2 (0 self)
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Abstract. We present a multicontext focused sequent calculus whose derivations are in bijective correspondence with normal natural deductions in the propositional fragment of the intuitionistic modal logic IS4. This calculus, suitable for the enumeration of normal proofs, is the starting point for the development of a sequent calculusbased bidirectional decision procedure for propositional IS4. In this system, relevant derived inference rules are constructed in a forward direction prior to proof search, while derivations constructed using these derived rules are searched over in a backward direction. We also present a variant which searches directly over normal natural deductions. Experimental results show that on most problems, the bidirectional prover is competitive with both conventional backward provers using loopdetection and inverse method provers, significantly outperforming them in a number of cases. 1
Countermodels from Sequent Calculi in MultiModal Logics
, 2012
"... A novel countermodelproducing decision procedure that applies to several multimodal logics, both intuitionistic and classical, is presented. Based on backwards search in labeled sequent calculi, the procedure employs a novel termination condition and countermodel construction. Using the procedure, ..."
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Cited by 1 (1 self)
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A novel countermodelproducing decision procedure that applies to several multimodal logics, both intuitionistic and classical, is presented. Based on backwards search in labeled sequent calculi, the procedure employs a novel termination condition and countermodel construction. Using the procedure, it is argued that multimodal variants of several classical and intuitionistic logics including K, T, K4, S4 and their combinations with D are decidable and have the finite model property. At least in the intuitionistic multimodal case, the decidability results are new. It is further shown that the countermodels produced by the procedure, starting from a set of hypotheses and no goals, characterize the atomic formulas provable from the hypotheses. 1
First International Workshop
"... Context interpretation and contextbased reasoning are key factors in the development of intelligent autonomous systems in a variety of applications. The ability to represent contextual factors, interpret them and combine them with other sources of knowledge are some of the challenges to enable inte ..."
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Context interpretation and contextbased reasoning are key factors in the development of intelligent autonomous systems in a variety of applications. The ability to represent contextual factors, interpret them and combine them with other sources of knowledge are some of the challenges to enable intelligent systems achieve correct behavior. Much work has been done in application areas that make use of contextual information, such as pervasive computing, logicbased sensor fusion and data integration. As well, the theoretical foundations for contextbased reasoning have been studied. However, there is still a great deal to do in context modeling, since generic context models for contextaware application development need to be further explored, as does the role of context reasoning with more recently emerging areas such as ontologies, including the semantic web, and approaches to belief change. Contextdependent data can arise from different sources; for example it may be gathered by sensors or collected from different knowledge or databases. The incompleteness and heterogenous nature of such data and the need for statebased context interpretation in dynamic systems suggest that nonmonotonic reasoning techniques can