172,422 research outputs found
PDL as a Multi-Agent Strategy Logic
Propositional Dynamic Logic or PDL was invented as a logic for reasoning
about regular programming constructs. We propose a new perspective on PDL as a
multi-agent strategic logic (MASL). This logic for strategic reasoning has
group strategies as first class citizens, and brings game logic closer to
standard modal logic. We demonstrate that MASL can express key notions of game
theory, social choice theory and voting theory in a natural way, we give a
sound and complete proof system for MASL, and we show that MASL encodes
coalition logic. Next, we extend the language to epistemic multi-agent
strategic logic (EMASL), we give examples of what it can express, we propose to
use it for posing new questions in epistemic social choice theory, and we give
a calculus for reasoning about a natural class of epistemic game models. We end
by listing avenues for future research and by tracing connections to a number
of other logics for reasoning about strategies.Comment: 10 pages, Poster presentation at TARK 2013 (arXiv:1310.6382)
http://www.tark.or
A dynamic-epistemic hybrid logic for intentions and information changes in strategic games
In this paper I present a dynamic-epistemic hybrid logic for reasoning about information and intention changes in situations of strategic interaction. I provide a complete axiomatization for this logic, and then use it to study intentions-based transformations of decision problems
An epistemic model of an agent who does not reflect on reasoning processes
This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent's reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. Key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. I also define an axiom system plus inference rules for knowledge- and unawareness statements whereby I drop the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach.Bounded Rationality, Knowledge, Unawareness, Epistemic Logic, Semantic Interpretation, Iterative Solution Concepts for Strategic Games
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
GDL Meets ATL: A Logic for Game Description and Strategic Reasoning
National audienceThis paper presents a logical framework that extends the Game Description Language with coalition operators from Alternating-time Temporal Logic and prioritised strategy connectives. Our semantics is built upon the standard state transition model. The new framework allows us to formalise van Benthem’s game-oriented principles in multi-player games, and formally derive Weak Determinacy and Zermelo’s Theorem for two-player games. We demonstrate with a real-world game how to use our language to specify a game and design a strategy, and how to use our framework to verify a winning/no-losing strategy. Finally, we show that the model-checking problem of our logic is in 2EXPTIME with respect to the size of game structure and the length of formula, which is no worse than the model-checking problem in ATL
Reasoning about Knowledge and Strategies under Hierarchical Information
Two distinct semantics have been considered for knowledge in the context of
strategic reasoning, depending on whether players know each other's strategy or
not. The problem of distributed synthesis for epistemic temporal specifications
is known to be undecidable for the latter semantics, already on systems with
hierarchical information. However, for the other, uninformed semantics, the
problem is decidable on such systems. In this work we generalise this result by
introducing an epistemic extension of Strategy Logic with imperfect
information. The semantics of knowledge operators is uninformed, and captures
agents that can change observation power when they change strategies. We solve
the model-checking problem on a class of "hierarchical instances", which
provides a solution to a vast class of strategic problems with epistemic
temporal specifications on hierarchical systems, such as distributed synthesis
or rational synthesis
Coalition Logic for Specification and Verification of Smart Contract Upgrades
Postponed access: the file will be available after 2023-11-12It has been argued in the literature that logics for reasoning about strategic abilities, and in particular coalition logic (CL), are well-suited for verification of properties of smart contracts on a blockchain. Smart contracts, however, can be upgraded by providing a new version of a contract on a new block. In this paper, we extend one of the recent formalisms for reasoning about updating CL models with a temporal modality connecting a newer version of a model to the previous one. In such a way, we make a step towards verification of properties of smart contracts with upgrades. We also discuss some properties of the resulting logic and the complexity of its model checking problem.acceptedVersio
Logics for strategic reasoning and collective decision-making
Strategic decision-making is ubiquitous in everyday life. The analysis of game strategies has been a research theme in game theory for several decades since von Neumann and Morgenstern. Sophisticated models and analysis tools have been developed with wide applications in Economics, Management Science, Social Science and Computer Science, especially in the field of Artificial Intelligence. However, \much of game theory is about the question whether strategic equilibria exist", as Johan van Benthem, a world-leading logician and game-theorist, points out, \but there are hardly any explicit languages for defining, comparing, or combining strategies". Without such a facility it is challenging for computer scientists to build intelligent agents that are capable of strategic decision-making. In the last twenty years, logical approaches have been proposed to tackle this problem. Pioneering work includes Game Logics, Coalition Logic and Alternating-time Temporal Logic (ATL). These logics either provide facilities for expressing and combining games or offer mechanisms for reasoning about strategic abilities of players. But none of them can solve the problem. The intrinsic difficulty in establishing such a logic is that reasoning about strategies requires combinations of temporal reasoning, counterfactual reasoning, reasoning about actions, preferences and knowledge, as well as reasoning about multi-agent interactions and coalitional abilities. More recently, a few new logical formalisms have been proposed by extending ATL with strategy variables in order to express strategies explicitly. However, most of these logics tend to have high computational complexity, because ATL introduces quantifications over strategies (functions), which leaves little hope of building any tractable inference system based on such a logic. This thesis takes up the challenge by using a bottom-up approach in order to create a balance between expressive power and computational efficiency. Instead of starting with a highly complicated logic, we propose a set of logical frameworks based on a simple and practical logical language, called Game Description Language (GDL), which has been used as an official language for General Game Playing (GGP) since 2005. To represent game strategies, we extend GDL with two binary prioritized connectives for combining actions in terms of their priorities specified by these connectives, and provide it with a semantics based on the standard state transition model. To reason about the strategic abilities of players, we further extend the framework with coalition operators from ATL for specifying the strategic abilities of players. More importantly, a unified semantics is provided for both GDL- and ATL- formulas, which allows us to verify and reason about game strategies. Interestingly, the framework can be used to formalize the fundamental game-playing principles and formally derive two well-known results on two-player games: Weak Determinacy and Zermelo's Theorem. We also show that the model-checking problem of the logic is not worse than that of ATL*, an extension of ATL. To deal with imperfect information games, we extend GDL with the standard epistemic operators and provide it with a semantics based on the epistemic state transition model. The language allows us to specify an imperfect information game and formalize its epistemic properties. Meanwhile, the framework allows us to reason about players' own as well as other players' knowledge during game playing. Most importantly, the logic has a moderate computational complexity, which makes it significantly different from similar existing frameworks. To investigate the interplay between knowledge shared by a group of players and its coalitional abilities, we provide a variant of semantics for ATL with imperfect information. The relation between knowledge sharing and coalitional abilities is investigated through the interplay of epistemic and coalition modalities. Moreover, this semantics is able to preserve the desirable properties of coalitional abilities. To deal with collective decision-making, we apply the approach of combining actions via their priorities for collective choice. We extend propositional logic with the prioritized connective for modelling reason-based individual and collective choices. Not only individual preferences but also aggregation rules can be expressed within this logic. A model-checking algorithm for this logic is thus developed to automatically generate individual and collective choices. In many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. We design an aggregation rule based on the priorities of individuals so as to investigate how the judgment from each individual affects group judgment in a hierarchical environment. We also show that this rule satisfies a set of plausible conditions and has a tractable computational complexity
Logics for strategic reasoning and collective decision-making
Strategic decision-making is ubiquitous in everyday life. The analysis of game strategies has been a research theme in game theory for several decades since von Neumann and Morgenstern. Sophisticated models and analysis tools have been developed with wide applications in Economics, Management Science, Social Science and Computer Science, especially in the field of Artificial Intelligence. However, \much of game theory is about the question whether strategic equilibria exist", as Johan van Benthem, a world-leading logician and game-theorist, points out, \but there are hardly any explicit languages for defining, comparing, or combining strategies". Without such a facility it is challenging for computer scientists to build intelligent agents that are capable of strategic decision-making. In the last twenty years, logical approaches have been proposed to tackle this problem. Pioneering work includes Game Logics, Coalition Logic and Alternating-time Temporal Logic (ATL). These logics either provide facilities for expressing and combining games or offer mechanisms for reasoning about strategic abilities of players. But none of them can solve the problem. The intrinsic difficulty in establishing such a logic is that reasoning about strategies requires combinations of temporal reasoning, counterfactual reasoning, reasoning about actions, preferences and knowledge, as well as reasoning about multi-agent interactions and coalitional abilities. More recently, a few new logical formalisms have been proposed by extending ATL with strategy variables in order to express strategies explicitly. However, most of these logics tend to have high computational complexity, because ATL introduces quantifications over strategies (functions), which leaves little hope of building any tractable inference system based on such a logic. This thesis takes up the challenge by using a bottom-up approach in order to create a balance between expressive power and computational efficiency. Instead of starting with a highly complicated logic, we propose a set of logical frameworks based on a simple and practical logical language, called Game Description Language (GDL), which has been used as an official language for General Game Playing (GGP) since 2005. To represent game strategies, we extend GDL with two binary prioritized connectives for combining actions in terms of their priorities specified by these connectives, and provide it with a semantics based on the standard state transition model. To reason about the strategic abilities of players, we further extend the framework with coalition operators from ATL for specifying the strategic abilities of players. More importantly, a unified semantics is provided for both GDL- and ATL- formulas, which allows us to verify and reason about game strategies. Interestingly, the framework can be used to formalize the fundamental game-playing principles and formally derive two well-known results on two-player games: Weak Determinacy and Zermelo's Theorem. We also show that the model-checking problem of the logic is not worse than that of ATL*, an extension of ATL. To deal with imperfect information games, we extend GDL with the standard epistemic operators and provide it with a semantics based on the epistemic state transition model. The language allows us to specify an imperfect information game and formalize its epistemic properties. Meanwhile, the framework allows us to reason about players' own as well as other players' knowledge during game playing. Most importantly, the logic has a moderate computational complexity, which makes it significantly different from similar existing frameworks. To investigate the interplay between knowledge shared by a group of players and its coalitional abilities, we provide a variant of semantics for ATL with imperfect information. The relation between knowledge sharing and coalitional abilities is investigated through the interplay of epistemic and coalition modalities. Moreover, this semantics is able to preserve the desirable properties of coalitional abilities. To deal with collective decision-making, we apply the approach of combining actions via their priorities for collective choice. We extend propositional logic with the prioritized connective for modelling reason-based individual and collective choices. Not only individual preferences but also aggregation rules can be expressed within this logic. A model-checking algorithm for this logic is thus developed to automatically generate individual and collective choices. In many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. We design an aggregation rule based on the priorities of individuals so as to investigate how the judgment from each individual affects group judgment in a hierarchical environment. We also show that this rule satisfies a set of plausible conditions and has a tractable computational complexity
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