175 research outputs found
Non-cooperative games with preplay negotiations
We consider an extension of strategic normal form games with a phase of negotiations before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, in order to provide additional incentives for each other to play designated strategies. Such offers are conditional on the recipients playing the specified strategies and they effect transformations of the payoff matrix of the game by accordingly transferring payoffs between players. We introduce and analyze solution concepts for 2-player normal form games with such preplay offers under various assumptions for the preplay negotiation phase and obtain results for existence of efficient negotiation strategies of the players. Then we extend the framework to coalitional preplay offers in N-player games, as well as to extensive form games with inter-play offers for side payments
Two-player preplay negotiation games with conditional offers
We consider an extension of strategic normal form games with a phase before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, contingent on the recipient playing the strategy indicated in the offer. Such offers transform the payoff matrix of the original game but preserve its non-cooperative nature. The type of offers we focus on here are conditional on a suggested 'matching offer' of the same kind made in return by the receiver. Players can exchange a series of such offers, thus engaging in a bargaining process before a strategic normal form game is played. In this paper we study and analyze solution concepts for two-player normal form games with such preplay negotiation phase, under several assumptions for the bargaining power of the players, such as the possibility of withdrawing previously made offers and opting out from the negotiation process, as well as the value of time for the players in such negotiations. We obtain results describing the possible solutions of such bargaining games and analyze the degrees of efficiency and fairness that can be achieved in such negotiation process
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
Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects
In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and results, and outline further research perspectives
Begin, After, and Later: a Maximal Decidable Interval Temporal Logic
Interval temporal logics (ITLs) are logics for reasoning about temporal
statements expressed over intervals, i.e., periods of time. The most famous ITL
studied so far is Halpern and Shoham's HS, which is the logic of the thirteen
Allen's interval relations. Unfortunately, HS and most of its fragments have an
undecidable satisfiability problem. This discouraged the research in this area
until recently, when a number non-trivial decidable ITLs have been discovered.
This paper is a contribution towards the complete classification of all
different fragments of HS. We consider different combinations of the interval
relations Begins, After, Later and their inverses Abar, Bbar, and Lbar. We know
from previous works that the combination ABBbarAbar is decidable only when
finite domains are considered (and undecidable elsewhere), and that ABBbar is
decidable over the natural numbers. We extend these results by showing that
decidability of ABBar can be further extended to capture the language
ABBbarLbar, which lays in between ABBar and ABBbarAbar, and that turns out to
be maximal w.r.t decidability over strongly discrete linear orders (e.g. finite
orders, the naturals, the integers). We also prove that the proposed decision
procedure is optimal with respect to the complexity class
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
Some Remarks on the Model Theory of Epistemic Plausibility Models
Classical logics of knowledge and belief are usually interpreted on Kripke
models, for which a mathematically well-developed model theory is available.
However, such models are inadequate to capture dynamic phenomena. Therefore,
epistemic plausibility models have been introduced. Because these are much
richer structures than Kripke models, they do not straightforwardly inherit the
model-theoretical results of modal logic. Therefore, while epistemic
plausibility structures are well-suited for modeling purposes, an extensive
investigation of their model theory has been lacking so far. The aim of the
present paper is to fill exactly this gap, by initiating a systematic
exploration of the model theory of epistemic plausibility models. Like in
'ordinary' modal logic, the focus will be on the notion of bisimulation. We
define various notions of bisimulations (parametrized by a language L) and show
that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type
result, and also two undefinability results. However, our main point is a
negative one, viz. that bisimulations cannot straightforwardly be generalized
to epistemic plausibility models if conditional belief is taken into account.
We present two ways of coping with this issue: (i) adding a modality to the
language, and (ii) putting extra constraints on the models. Finally, we make
some remarks about the interaction between bisimulation and dynamic model
changes.Comment: 19 pages, 3 figure
Optimal Tableaux Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-time Temporal Logic ATL+
We develop a sound, complete and practically implementable tableaux-based
decision method for constructive satisfiability testing and model synthesis in
the fragment ATL+ of the full Alternating time temporal logic ATL*. The method
extends in an essential way a previously developed tableaux-based decision
method for ATL and works in 2EXPTIME, which is the optimal worst case
complexity of the satisfiability problem for ATL+ . We also discuss how
suitable parametrizations and syntactic restrictions on the class of input ATL+
formulae can reduce the complexity of the satisfiability problem.Comment: 45 page
Complete and Terminating Tableau for the Logic of Proper Subinterval Structures over Dense Orderings
We introduce special pseudo-models for the interval logic of proper subintervals over dense linear orderings. We prove finite model property with respect to such pseudo-models, and using that result we develop a decision procedure based on a sound, complete, and terminating tableau for that logic. The case of proper subintervals is essentially more complicated than the case of strict subintervals, for which we developed a similar tableau-based decision procedure in a recent work
An Optimal Decision Procedure for MPNL over the Integers
Interval temporal logics provide a natural framework for qualitative and
quantitative temporal reason- ing over interval structures, where the truth of
formulae is defined over intervals rather than points. In this paper, we study
the complexity of the satisfiability problem for Metric Propositional Neigh-
borhood Logic (MPNL). MPNL features two modalities to access intervals "to the
left" and "to the right" of the current one, respectively, plus an infinite set
of length constraints. MPNL, interpreted over the naturals, has been recently
shown to be decidable by a doubly exponential procedure. We improve such a
result by proving that MPNL is actually EXPSPACE-complete (even when length
constraints are encoded in binary), when interpreted over finite structures,
the naturals, and the in- tegers, by developing an EXPSPACE decision procedure
for MPNL over the integers, which can be easily tailored to finite linear
orders and the naturals (EXPSPACE-hardness was already known).Comment: In Proceedings GandALF 2011, arXiv:1106.081
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