162 research outputs found
The Basic Algebra of Game Equivalences
We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities. En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways game identities into modal formulae. The completeness proof is based on reduction of game terms to a certain 'minimal canonical form', by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities
Transformations of normal form games by preplay offers for payments among players
We consider transformations of normal form games by binding preplay offers of
players for payments of utility to other players conditional on them playing
designated in the offers strategies. The game-theoretic effect of such preplay
offers is transformation of the payoff matrix of the game by transferring
payoffs between players. Here we analyze and completely characterize the
possible transformations of the payoff matrix of a normal form game by sets of
preplay offers.Comment: 17 pages, under submissio
From Linear to Branching-Time Temporal Logics: Transfer of Semantics and Definability
This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in tree
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
Secure aggregation of distributed information: How a team of agents can safely share secrets in front of a spy
We consider the generic problem of Secure Aggregation of Distributed
Information (SADI), where several agents acting as a team have information
distributed among them, modeled by means of a publicly known deck of cards
distributed among the agents, so that each of them knows only her cards. The
agents have to exchange and aggregate the information about how the cards are
distributed among them by means of public announcements over insecure
communication channels, intercepted by an adversary "eavesdropper", in such a
way that the adversary does not learn who holds any of the cards. We present a
combinatorial construction of protocols that provides a direct solution of a
class of SADI problems and develop a technique of iterated reduction of SADI
problems to smaller ones which are eventually solvable directly. We show that
our methods provide a solution to a large class of SADI problems, including all
SADI problems with sufficiently large size and sufficiently balanced card
distributions
Game-Theoretic Semantics for Alternating-Time Temporal Logic
We introduce versions of game-theoretic semantics (GTS) for Alternating-Time
Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a
winning strategy in a semantic evaluation game, and thus the game-theoretic
perspective appears in the framework of ATL on two semantic levels: on the
object level in the standard semantics of the strategic operators, and on the
meta-level where game-theoretic logical semantics is applied to ATL. We unify
these two perspectives into semantic evaluation games specially designed for
ATL. The game-theoretic perspective enables us to identify new variants of the
semantics of ATL based on limiting the time resources available to the verifier
and falsifier in the semantic evaluation game. We introduce and analyse an
unbounded and (ordinal) bounded GTS and prove these to be equivalent to the
standard (Tarski-style) compositional semantics. We show that in these both
versions of GTS, truth of ATL formulae can always be determined in finite time,
i.e., without constructing infinite paths. We also introduce a non-equivalent
finitely bounded semantics and argue that it is natural from both logical and
game-theoretic perspectives.Comment: Preprint of a paper published in ACM Transactions on Computational
Logic, 19(3): 17:1-17:38, 201
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