Reasoning about types of action and agent capabilities

Hartonas, Chrysafis

doi:10.1093/jigpal/jzs045

Cited by 3 publications

(20 citation statements)

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“…and, as detailed in [Har13], these equivalences reveal the naturalness of precondition-effect process type operator.…”

Section: Preliminariesmentioning

confidence: 79%

“…We adopt a slightly different notation from the one usually met in the literature and we write AA for A; A, A + A for A ∪ A, and ϕ for ϕ?, when ϕ acts as a program. Moreover, we write ∀A.ϕ for the familiar boxed formula [A]ϕ in order to stay consistent with the notation in [Har13], where it received a non-standard, type interpretation. The possibility operator and the propositional connectives are not taken as primitive, but they can be defined as usual (e.g.…”

Section: Syntax and Intuitive Semanticsmentioning

confidence: 99%

“…We trust that the reader is familiar with the standard relational interpretation of the language of PDL. In [Har13] and [Har14], τPDL has received two kinds of interpretations: a type interpretation and a standard relational one. In [Har14], the two interpretations are shown to be equivalent, meaning that exactly the same formulas are validated in the two classes of models.…”

Section: Syntax and Intuitive Semanticsmentioning

confidence: 99%

“…In [Har14], the two interpretations are shown to be equivalent, meaning that exactly the same formulas are validated in the two classes of models. In [Har13], a set AtP of basic types, test types and precondition-effect types are considered and then complex process types are built by using the regular operators of composition, choice and Kleene star. The precondition-effect program terms ϕ ⇒ ψ can be viewed as anonymous processes/actions or as a type of processes/actions.…”

Section: Syntax and Intuitive Semanticsmentioning

confidence: 99%

“…We choose here not to deal with the backward possibility operator. First, as argued in [Har13], the specific construct is a weak form of the well-known converse operator which has been successfully handled for CPDL in [GW10,Wid10]. Second, the converse, as well as the backwards possibility operator, has a significant impact on the design of a decision procedure, as it is revealed by [GW09] and [GW10] for PDL and CPDL, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Tableaux for type PDL

Kritsimallis¹,

Hartonas

2013

Proceedings of the 6th Balkan Conference in Informatics

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The system of Type PDL (τPDL) is an extension of Propositional Dynamic Logic (PDL) and its main goal is to provide a formal basis for reasoning about types of actions (modeled by their preconditions and effects) and agent capabilities. The system has two equivalent interpretations, namely the standard relational semantics and the type semantics, where process terms are interpreted as types, i.e. sets of binary relations. Its satisfiability problem is decidable, as a NE T decision procedure was provided based on a filtration argument and it was suggested that the satisfiability problem for τPDL should be solvable in deterministic, single exponential time. In this paper, we address the problem of the complexity of the satisfiability problem of τPDL. We present a deterministic tableau-based satisfiability algorithm and prove that it is sound and complete and that it runs in E T . Additionally, the algorithm detects satisfiability as earlier as possible, by restricting or-branching whenever possible. IntroductionThe satisfiability problem of Propositional Dynamic Logic (PDL) [FL79, HKT00]) is E T -complete. Various decision procedures have been given such as best-case exponential [Pra79], working in multiple stages [Pra80, NS09], on-the-fly [GM00, AGW09] and with analytic cut-rule for the converse [GM00, NS09], most of them based on and-or tableaux [Gor14]. The algorithm of [GW09] for PDL and its extension for the converse (CPDL) [GW10] reveal the crucial role that global caching plays to the achievement of an optimal algorithm.The system of τPDL (Type PDL) [Har13, Har14] is an extension of PDL. The main goal of such a system is to provide a formal basis for reasoning about types of actions instead of merely actions. As described in [Har13], the system is inspired by the OWL-S process model of services [MBH + 04], where concrete actions are hidden from public view and what is publicly known is only the type of actions a service can perform, modeled by their preconditions and effects. Syntactically, the language of τPDL extends that of PDL with abstract process types designated by their preconditions and effects, written in the form ϕ ⇒ ψ, with agent capabilities statements C ı A which declare that agent ı can do A and with a backwards possibility operator, a weak form of converse.The interpretation of the introduced system of τPDL in [Har13] is different from the standard PDL semantics. As the main motivation of τPDL is reasoning about types of processes, type semantics has been proposed where process terms are interpreted as types, i.e. sets of binary relations. On the other hand, in [Har14], it was shown that the standard relational semantics is equivalent to the type semantics.As far as the capabilities operator is concerned, the semantic options made in [Har13, Har14] are slightly different from those made in the KARO Framework [vdHvLM94,vdHvLM99,vdHW03] and it is that difference in semantics, as detailed in [Har13, Har14] that allows for a finitary axiomatization and a decidability proof, provided in [Har13, Har...

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“…and, as detailed in [Har13], these equivalences reveal the naturalness of precondition-effect process type operator.…”

Section: Preliminariesmentioning

confidence: 79%

Section: Syntax and Intuitive Semanticsmentioning

confidence: 99%