Global Numerical Constraints on Trees

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence

Relentful Strategic Reasoning in 1 Alternating-Time Temporal Logic

Temporal logics are a well investigated formalism for the specification, verification, and synthesis of reactive systems. Within this family, Alternating-Time Temporal Logic (ATL , for short) has been introduced as a useful generalization of classical linear- and branching-time temporal logics, by allowing temporal operators to be indexed by coalitions of agents. Classically, temporal logics are memoryless: once a path in the computation tree is quantified at a given node, the computation that has led to that node is forgotten. Recently, mCTL has been defined as a memoryful variant of CTL , where path quantification is memoryful. In the context of multi-agent planning, memoryful quantification enables agents to “relent” and change their goals and strategies depending on their history. In this paper, we define mATL , a memoryful extension of ATL , in which a formula is satisfied at a certain node of a path by taking into account both the future and the past. We study the expressive power of mATL , its succinctness, as well as related decision problems. We also investigate the relationship between memoryful quantification and past modalities and show their equivalence. We show that both the memoryful and the past extensions come without any computational price; indeed, we prove that both the satisfiability and the model-checking problems are 2EXPTIME-COMPLETE, as they are for AT

Reasoning About Strategies: On the Model-Checking Problem

In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL\star, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHP-SL, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the very specific setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems. In this paper, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multi-agent concurrent games. We prove that SL includes CHP-SL, while maintaining a decidable model-checking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHP-SL. Moreover, we prove that such a problem for SL is NonElementarySpace-hard. This negative result has spurred us to investigate here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of obtaining an elementary model-checking problem. Among the others, we study the sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, a single goal at a time. About these logics, we prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not harder than the one for ATL\star

Quantifying Over Trees in Monadic Second-Order Logic

Monadic Second-Order Logic (MSO) extends FirstOrder Logic ( FO) with variables ranging over sets and quantifications over those variables. We introduce and study Monadic Tree Logic (MTL), a fragment of MSO interpreted on infinitetree models, where the sets over which the variables range are arbitrary subtrees of the original model. We analyse the expressiveness of MTL compared with variants of MSO and MPL, namely MSO with quantifications over paths. We also discuss the connections with temporal logics, by providing non-trivial fragments of the Graded mu-CALCULUS that can be embedded into MTL and by showing that MTL is enough to encode temporal logics for reasoning about strategies with FO-definable goals

Strategic Offering of a Price Maker Wind Power Producer in Distribution-Level Energy Markets in Presence of Flexible Prosumers

This paper presents an optimal bidding strategy for a strategic wind power producer (WPP) in a distribution-level energy market (DLEM). The behavior of the WPP is modelled through a bi-level stochastic optimization problem where the upper-level problem maximizes the profit of the WPP and the lower-level problem describes the clearing processes of the DLEM while considering network constraints. The bi-level problem is a stochastic mathematical program with equilibrium constraints (MPEC) that is formulated as a mixed-integer linear programming (MILP) problem. The main focus of this study is investigating prosumers’ impact on the market power of the strategic WPP in a DLEM structure. In this model, the effect of flexible prosumers from the aspects of demand response (DR) participants and photovoltaic penetration level (PVPL) on the WPP’s offering strategy is investigated. Moreover, the impact of bilateral contract on the market power of the strategic WPP and the cleared prices of the network is addressed. The proposed model is implemented in an IEEE 33-bus and numerical results illustrate how behavior of flexible prosumers and PVPL index affect the decision making of the strategic WPP when network constraints are considered. Numerical results show that by active participation of prosumers in DR programs, the reliance of DLEM on the strategic WPP reduces. Moreover, if the WPP participates in bilateral contracts, its offering to the DELM decreases, and as the result, the cleared prices augment indicating market power of the WPP.© 2022 Authors. Published by IEEE. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/fi=vertaisarvioitu|en=peerReviewed

Sublogics of a Branching Time Logic of Robustness

In this paper we study sublogics of RoCTL*, a recently proposed logic for specifying robustness. RoCTL* allows specifying robustness in terms of properties that are robust to a certain number of failures. RoCTL* is an extension of the branching time logic CTL* which in turn extends CTL by removing the requirement that temporal operators be paired with path quantifiers. In this paper we consider three sublogics of RoCTL*. We present a tableau for RoBCTL*, a bundled variant of RoCTL* that allows fairness constraints to be placed on allowable paths. We then examine two CTL-like restrictions of CTL*. Pair-RoCTL* requires a temporal operator to be paired with a path quantifier; we show that Pair-RoCTL* is as hard to reason about as the full CTL*. State-RoCTL* is restricted to State formulas, and we show that there is a linear truth preserving translation of State-RoCTL into CTL, allowing State-RoCTL to be reasoned about as efficiently as CTL

Strategic Reasoning in Game Theory

Game theory in AI is a powerful mathematical framework largely applied in the last three decades for the strategic reasoning in multi-agent systems. Seminal works along this line started with turn-based two-player games (under perfect and imperfect information) to check the correctness of a system against an unpredictable environment. Then, large effort has been devoted to extend those works to the multi-agent setting and, specifically, to efficiently reasoning about important solution concepts such as Nash Equilibria and the like. Breakthrough contributions along this direction concern the introduction of logics for the strategic reasoning such as Alternating-time Temporal Logic (ATL), Strategy Logic (SL), and their extensions. Two-player games and logics for the strategic reasoning are nowadays very active areas of research. In this thesis we significantly advance the work along both these two lines of research by providing fresh studies and results of practical application. We start with two-player reachability games and first investigate the problem of checking whether a designed player has more than a winning strategy to reach a target. We investigate this question under both perfect and imperfect information. We provide an automata-based solution that requires linear-time, in the perfect information setting, and exponential-time, in the imperfect one. In both cases, the results are tight. Then, we move to multi-player concurrent games and study the following specific setting: (i) Player_0's objective is to reach a target W, and (ii) the opponents are trying to stop this but have partial observation about Player_0's actions. We study the problem of deciding whether the opponents can prevent Player_0 to reach W. We show, using an automata-theoretic approach that, assuming the opponents have the same partial observation and play under uniformity, the problem is in ExpTime. We recall that, in general, multi-player reachability games with imperfect information are undecidable. Then, we move to the more expressive framework of logics for the strategic reasoning. We first introduce and study two graded extensions of SL, namely GSL and GradedSL. By the former, we define a graded version over single strategy variables, i.e. "there exist at least g different strategies", where the strategies are counted semantically. We study the model checking-problem for GSL and show that for its fragment called vanilla GSL[1G] the problem is PTime-complete. By GradedSL, we consider a graded version over tuple of strategy variables and use a syntactic counting over strategies. By means of GradedSL we show how to count the number of different strategy profiles that are Nash equilibria (NE). By analyzing the structure of the specific formulas involved, we conclude that the important problem of checking for the existence of a unique NE can be solved in 2ExpTime, which is not harder than merely checking for the existence of such an equilibrium. Finally, we adopt the view of bounded rationality, and look only at "simple" strategies in specifications of agents’ abilities. We formally define what "simple" means, and propose a variant of plain ATL, namely NatATL, that takes only such strategies into account. We study the model checking problem for the resulting semantics of ability and obtain tight results. The positive results achieved with NatATL encourage for the investigation of simple strategies over more powerful logics, including SL