446 research outputs found
Tableau-based decision procedure for the multi-agent epistemic logic with operators of common and distributed knowledge
We develop an incremental-tableau-based decision procedure for the
multi-agent epistemic logic MAEL(CD) (aka S5_n (CD)), whose language contains
operators of individual knowledge for a finite set Ag of agents, as well as
operators of distributed and common knowledge among all agents in Ag. Our
tableau procedure works in (deterministic) exponential time, thus establishing
an upper bound for MAEL(CD)-satisfiability that matches the (implicit)
lower-bound known from earlier results, which implies ExpTime-completeness of
MAEL(CD)-satisfiability. Therefore, our procedure provides a complexity-optimal
algorithm for checking MAEL(CD)-satisfiability, which, however, in most cases
is much more efficient. We prove soundness and completeness of the procedure,
and illustrate it with an example.Comment: To appear in the Proceedings of the 6th IEEE Conference on Software
Engineering and Formal Methods (SEFM 2008
Reducing Validity in Epistemic ATL to Validity in Epistemic CTL
We propose a validity preserving translation from a subset of epistemic
Alternating-time Temporal Logic (ATL) to epistemic Computation Tree Logic
(CTL). The considered subset of epistemic ATL is known to have the finite model
property and decidable model-checking. This entails the decidability of
validity but the implied algorithm is unfeasible. Reducing the validity problem
to that in a corresponding system of CTL makes the techniques for automated
deduction for that logic available for the handling of the apparently more
complex system of ATL.Comment: In Proceedings SR 2013, arXiv:1303.007
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
We show that Branching-time temporal logics CTL and CTL*, as well as
Alternating-time temporal logics ATL and ATL*, are as semantically expressive
in the language with a single propositional variable as they are in the full
language, i.e., with an unlimited supply of propositional variables. It follows
that satisfiability for CTL, as well as for ATL, with a single variable is
EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a
single variable is 2EXPTIME-complete,--i.e., for these logics, the
satisfiability for formulas with only one variable is as hard as satisfiability
for arbitrary formulas.Comment: Prefinal version of the published pape
Tableau-based decision procedure for the multi-agent epistemic logic with all coalitional operators for common and distributed knowledge
We develop a conceptually clear, intuitive, and feasible decision procedure
for testing satisfiability in the full multi-agent epistemic logic CMAEL(CD)
with operators for common and distributed knowledge for all coalitions of
agents mentioned in the language. To that end, we introduce Hintikka structures
for CMAEL(CD) and prove that satisfiability in such structures is equivalent to
satisfiability in standard models. Using that result, we design an incremental
tableau-building procedure that eventually constructs a satisfying Hintikka
structure for every satisfiable input set of formulae of CMAEL(CD) and closes
for every unsatisfiable input set of formulae.Comment: Substantially extended and corrected version of arXiv:0902.2125. To
appear in: Logic Journal of the IGPL, special issue on Formal Aspects of
Multi-Agent System
Coalition logic with individual, distributed and common knowledge
Coalition logic is currently one of the most popular logics for multi-agent systems. While logics combining coalitional and epistemic operators have received considerable attention, completeness results for epistemic extensions of coalition logic have so far been missing. In this paper we provide several such results and proofs.We prove completeness for epistemic coalition logic with common knowledge, with distributed knowledge, and with both common and distributed knowledge, respectively. Furthermore, we completely characterise the complexity of the satisfiability problem for each of the three logics. We also study logics with interaction axioms connecting coalitional ability and knowledge
Complexity results for modal logic with recursion via translations and tableaux
This paper studies the complexity of classical modal logics and of their
extension with fixed-point operators, using translations to transfer results
across logics. In particular, we show several complexity results for
multi-agent logics via translations to and from the -calculus and modal
logic, which allow us to transfer known upper and lower bounds. We also use
these translations to introduce a terminating tableau system for the logics we
study, based on Kozen's tableau for the -calculus, and the one of Fitting
and Massacci for modal logic. Finally, we show how to encode the tableaux we
introduced into -calculus formulas. This encoding provides upper bounds
for the satisfiability checking of the few logics we previously did not have
algorithms for.Comment: 43 pages. arXiv admin note: substantial text overlap with
arXiv:2209.1037
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