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

Game-Theoretic Semantics for ATL+ with Applications to Model Checking

We develop a game-theoretic semantics (GTS) for the fragment ATL(+) of the alternating-time temporal logic ATL*, thereby extending the recently introduced GTS for ATL. We show that the game-theoretic semantics is equivalent to the standard compositional semantics of ATL(+) with perfect-recall strategies. Based on the new semantics, we provide an analysis of the memory and time resources needed for model checking ATL(+) and show that strategies of the verifier that use only a very limited amount of memory suffice. Furthermore, using the GTS, we provide a new algorithm for model checking ATL(+) and identify a natural hierarchy of tractable fragments of ATL(+) that substantially extend ATL. (C) 2020 Elsevier Inc. All rights reserved.Peer reviewe

Model checking coalitional games in shortage resource scenarios

Verification of multi-agents systems (MAS) has been recently studied taking into account the need of expressing resource bounds. Several logics for specifying properties of MAS have been presented in quite a variety of scenarios with bounded resources. In this paper, we study a different formalism, called Priced Resource-Bounded Alternating-time Temporal Logic (PRBATL), whose main novelty consists in moving the notion of resources from a syntactic level (part of the formula) to a semantic one (part of the model). This allows us to track the evolution of the resource availability along the computations and provides us with a formalisms capable to model a number of real-world scenarios. Two relevant aspects are the notion of global availability of the resources on the market, that are shared by the agents, and the notion of price of resources, depending on their availability. In a previous work of ours, an initial step towards this new formalism was introduced, along with an EXPTIME algorithm for the model checking problem. In this paper we better analyze the features of the proposed formalism, also in comparison with previous approaches. The main technical contribution is the proof of the EXPTIME-hardness of the the model checking problem for PRBATL, based on a reduction from the acceptance problem for Linearly-Bounded Alternating Turing Machines. In particular, since the problem has multiple parameters, we show two fixed-parameter reductions.Comment: In Proceedings GandALF 2013, arXiv:1307.416

CTL with Finitely Bounded Semantics

We consider a variation of the branching time logic CTL with non-standard, "finitely bounded" semantics (FBS). FBS is naturally defined as game-theoretic semantics where the proponent of truth of an eventuality must commit to a time limit (number of transition steps) within which the formula should become true on all (resp. some) paths starting from the state where the formula is evaluated. The resulting version CTL(FB) of CTL differs essentially from the standard one as it no longer has the finite model property. We develop two tableaux systems for CTL(FB). The first one deals with infinite sets of formulae, whereas the second one deals with finite sets of formulae in a slightly extended language allowing explicit indication of time limits in formulae. We prove soundness and completeness of both systems and also show that the latter tableaux system provides an EXPTIME decision procedure for it and thus prove EXPTIME-completeness of the satisfiability problem