A stit-Logic for Extensive Form Group Strategies

arXiv preprint arXiv:1202.1309, 2012

Abstract: Strategy Logic (SL, for short) has been recently introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns to be very powerful, subsuming all major previously studied modal logics for strategic reasoning, including ATL, ATL*, and the like. Unfortunately, due to its expressiveness, SL has a non-elementarily decidable model-checking problem and a highly undecidable satisfiability problem, specifically, $\ Sigma_ { ...

Log. Methods Comput. Sci., 2017

Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very powerful, subsuming all major previously studied modal logics for strategic reasoning, including ATL, ATL*, and the like. Unfortunately, due to its high expressiveness, SL has a non-elementarily decidable model-checking problem and the satisfiability question is undecidable, specifically Sigma_1^1. In order to obtain a decidable sublogic, we introduce and study here One-Goal Strategy Logic (SL[1G], for short). This is a syntactic fragment of SL, strictly subsuming ATL*, which encompasses formulas in prenex normal form having a single temporal goal at a time, for every strategy quantification of agents. We prove that, unlike SL, SL[1G] has the bounded tree-model property and its satisfiability problem is decidable in 2ExpTime, thus not harder than the ...

Lecture Notes in Computer Science, 2009

This paper presents a complete temporal STIT logic for reasoning about multi-agency. I discuss its application for reasoning about norms, knowledge, autonomy, and other multi-agent concepts. Also I give some arguments in favor of taking STIT formalisms instead of dynamic logics as the basis for logics for representing multi-agent system concepts.

Journal of Logic and Computation, 2006

Seeing To It That (STIT) logic is a logic of agency, proposed in the 1990s in the domain of philosophy of action. It is the logic of constructions of the form 'agent a sees to it that ''. We believe that STIT theory can contribute to the logical analysis of multiagent systems. To support this claim, we show that there is a close relationship with more recent logics for multiagent systems. This work extends Broersen et al. (2006, Electron Notes Theor. Comput. Sci., Vol. 157, pp. 23-35) where we presented a translation from Pauly's Coalition Logic to Chellas' STIT logic. Here we focus on Alur, Henzinger and Kupferman's Alternating-time Temporal Logic (ATL), and the logic of the 'fused' s ½ scstit : operator for strategic ability, as described by Horty. After a brief presentation of ATL and the definition of a discrete-time strategic STIT framework slightly adapted from Horty, we give a translation from ATL to the STIT framework, and prove that it determines correct embedding.

Lecture Notes in Computer Science, 2012

We propose a variant of Alternating-time Temporal Logic (ATL) grounded in the agents' operational know-how, as defined by their libraries of abstract plans. Inspired by ATLES, a variant itself of ATL, it is possible in our logic to explicitly refer to "rational" strategies for agents developed under the Belief-Desire-Intention agent programming paradigm. This allows us to express and verify properties of BDI systems using ATL-type logical frameworks.

Electronic Notes in Theoretical Computer Science, 2006

STIT is a logic of agency that has been proposed in the nineties in the domain of philosophy of action. It is the logic of constructions of the form "agent a sees to it that ϕ". We believe that STIT theory may contribute to the logical analysis of multiagent systems. To support this claim, in this paper we show that there is a close relationship with more recent logics for multiagent systems. We focus on Pauly's Coalition Logic and the logic of the cstit operator, as described by Horty. After a brief presentation of Coalition Logic and a discrete-time version (including a next operator) of the STIT framework, we introduce a translation from Coalition Logic to the discrete STIT logic, and prove that it is correct.

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, 2019

In this paper we introduce Strategy Logic with simple goals (SL[SG]), a fragment of Strategy Logic that strictly extends the well-known Alternating-time Temporal Logic ATL by introducing arbitrary quantification over the agents' strategies. Our motivation comes from game-theoretic applications, such as expressing Stackelberg equilibria in games, coercion in voting protocols, as well as module checking for simple goals. Most importantly, we prove that the model checking problem for SL[SG] is PTIME-complete, the same as ATL. Thus, the extra expressive power comes at no computational cost as far as verification is concerned.

Lecture Notes in Computer Science, 2014

Starting from the seminal work introducing Alternating Temporal Logic, formalisms for strategic reasoning have assumed a prominent role in multi-agent systems verification. Among the others, Strategy Logic (SL) allows to represent sophisticated solution concepts, by treating agent strategies as first-order objects. A drawback from the high power of SL is to admit non-behavioral strategies: a choice of an agent, at a given point of a play, may depend on choices other agents can make in the future or in counterfactual plays. As the latter moves are unpredictable, such strategies cannot be easily implemented, making the use of the logic problematic in practice. In this paper, we describe a hierarchy of SL fragments as syntactic restrictions of the recently defined Boolean-Goal Strategy Logic (SL[bg]). Specifically, we introduce Alternating-Goal Strategy Logic (SL[ag]) that, by imposing a suitable alternation over the nesting of the Boolean connectives in SL[bg], induces two dual chains of sets of formulas, the conjunctive and disjunctive ones. A formula belongs to the level i of the conjunctive chain if it just contains conjunctions of atomic goals together with a unique formula belonging to the disjunctive chain of level i − 1. The disjunctive chain is defined similarly. We formally prove that classic and behavioral semantics for SL [ag] coincide. Additionally, we study the related model-checking problem showing that it is 2ExpTime-complete.

Logique at Analyse, 2017

In this paper we establish equivalence results for the different semantics for the temporal STIT logic T-STIT, that includes temporal operators and the group agency operator for the grand coalition, and we study a semantics for temporal STIT that is based on the concept of interpreted system a la Fagin et al. We discuss the descriptive adequacy of the above semantics in capturing a given game-theoretical scenario where information about the players is included, and we compare them with traditional BT+AC semantics. Also, we discuss the extension of T-STIT with full groups and the corresponding operators, and we discuss the distinction between frames that impose additivity and superadditivity on the choices of arbitrary groups.

Synthese, 2000

We draw parallels between several closely related logics that combine -in different proportions -elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly in 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der . In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL.