arXiv subjects

Valentin Goranko

Publications and source records attributed to Valentin Goranko.

At least 19 recordsLinked to original sources

arXiv2023

Structural theory of trees. I. Branching and condensations of trees

Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of \emph{condensed trees}, which are trees in which every node is a branching node. We then introduce and investigate two different constructions of \emph{tree condensations} -- one shrinking, and the other expanding, the tree to a condensed tree.

math.CO↗

arXiv2023

Structural theory of trees. II. Completeness and completions of trees

Trees are partial orderings where every element has a linearly ordered set of smaller elements. We define and study several natural notions of completeness of trees, extending Dedekind completeness of linear orders and Dedekind-MacNeille completions of partial orders. We then define constructions of \emph{tree completions} that extend any tree to a minimal one satisfying the respective completeness property.

math.CO↗

arXiv2022

The temporal logic of coalitional goal assignments in concurrent multi-player games

We introduce and study a natural extension of the Alternating time temporal logic ATL, called Temporal Logic of Coalitional Goal Assignments (TLCGA). It features just one, but quite expressive, coalitional strategic operator, viz. the coalitional goal assignment operator, which is based on a mapping assigning to each set of players in the game its coalitional goal, formalised by a path formula of the language of TLCGA, i.e. a formula prefixed with a temporal operator X,U, or G, representing a temporalised objective for the respective coalition, describing the property of the plays on which that objective is satisfied. We establish fixpoint characterizations of the temporal goal assignments in a mu-calculus extension of TLCGA, discuss its expressiveness and illustrate it with some examples, prove bisimulation invariance and Hennessy-Milner property for it with respect to a suitably defined notion of bisimulation, construct a sound and complete axiomatic system for TLCGA, and obtain its decidability via finite model property.

cs.LO↗

arXiv2021

Knowledge-Based Strategies for Multi-Agent Teams Playing Against Nature

We study teams of agents that play against Nature towards achieving a common objective. The agents are assumed to have imperfect information due to partial observability, and have no communication during the play of the game. We propose a natural notion of higher-order knowledge of agents. Based on this notion, we define a class of knowledge-based strategies, and consider the problem of synthesis of strategies of this class. We introduce a multi-agent extension, MKBSC, of the well-known Knowledge-Based Subset Construction applied to such games. Its iterative applications turn out to compute higher-order knowledge of the agents. We show how the MKBSC can be used for the design of knowledge-based strategy profiles and investigate the transfer of existence of such strategies between the original game and in the iterated applications of the MKBSC, under some natural assumptions. We also relate and compare the "intensional" view on knowledge-based strategies based on explicit knowledge representation and update, with the "extensional" view on finite memory strategies based on finite transducers and show that, in a certain sense, these are equivalent.

cs.MA↗

arXiv2021

Rational coordination with no communication or conventions

We study pure coordination games where in every outcome, all players have identical payoffs, 'win' or 'lose'. We identify and discuss a range of 'purely rational principles' guiding the reasoning of rational players in such games and analyze which classes of coordination games can be solved by such players with no preplay communication or conventions. We observe that it is highly nontrivial to delineate a boundary between purely rational principles and other decision methods, such as conventions, for solving such coordination games.

cs.MA↗

arXiv2021

A Logic for Conditional Local Strategic Reasoning

We consider systems of rational agents who act and interact in pursuit of their individual and collective objectives. We study and formalise the reasoning of an agent, or of an external observer, about the expected choices of action of the other agents based on their objectives, in order to assess the reasoner's ability, or expectation, to achieve their own objective. To formalize such reasoning we extend Pauly's Coalition Logic with three new modal operators of conditional strategic reasoning, thus introducing the Logic for Local Conditional Strategic Reasoning ConStR. We provide formal semantics for the new conditional strategic operators in concurrent game models, introduce the matching notion of bisimulation for each of them, prove bisimulation invariance and Hennessy-Milner property for each of them, and discuss and compare briefly their expressiveness. Finally, we also propose systems of axioms for each of the basic operators of ConStR and for the full logic.

cs.GT↗

arXiv2020

Model checking and model synthesisfrom partial models: a logic-based perspective

I consider the following generic scenario: an abstract model M of some 'real' system is only partially presented, or partially known to us, and we have to ensure that the actual system satisfies a given specification, formalised in some logical language. This scenario has at least two essentially different interpretations, leading to two, essentially different, formal logical and algorithmic problems: "Model Synthesis from Partial Models", where some 'admissible' extension of M to a full model must satisfy the specification, and "Model Checking of Partial Models", where all 'admissible' extensions of M to a full model must satisfy the specification. These problems naturally extend the classical logical decision problems of Satisfiability, Validity, and Model Checking. Here I briefly discuss both problems in the contexts of classical, modal and temporal logics. I make some observations, state some open questions, and outline a general tableaux-style procedure that solves the problem of unconstrained model synthesis from finite partial models for several well-known modal and temporal logics, incl. K, LTL, CTL, ATL.

cs.LO↗

arXiv2020

Logic-based Specification and Verification of Homogeneous Dynamic Multi-agent Systems

We develop a logic-based framework for formal specification and algorithmic verification of homogeneous and dynamic concurrent multi-agent transition systems (HDMAS). Homogeneity means that all agents have the same available actions at any given state and the actions have the same effects regardless of which agents perform them. The state transitions are therefore determined only by the vector of numbers of agents performing each action and are specified symbolically, by means of conditions on these numbers definable in Presburger arithmetic. The agents are divided into controllable (by the system supervisor/controller) and uncontrollable, representing the environment or adversary. Dynamicity means that the numbers of controllable and uncontrollable agents may vary throughout the system evolution, possibly at every transition. As a language for formal specification we use a suitably extended version of Alternating-time Temporal Logic (ATL), where one can specify properties of the type "a coalition of (at least) $n$ controllable agents can ensure against (at most) $m$ uncontrollable agents that any possible evolution of the system satisfies a given objective $φ$", where $φ$ is specified again as a formula of that language and each of $n$ and $m$ is either a fixed number or a variable that can be quantified over. We provide formal semantics to our logic $\mathcal{L}_{HDMAS}$ and define normal form of its formulae. We then prove that every formula in $\mathcal{L}_{HDMAS}$ is equivalent in the finite to one in a normal form and develop an algorithm for global model checking of formulae in normal form in finite HDMAS models, which invokes model checking truth of Presburger formulae. We establish worst case complexity estimates for the model checking algorithm and illustrate it on a running example.

cs.LO↗

arXiv2019

Tableau-based decision procedure for full coalitional multiagent temporal-epistemic logic of linear time

We develop a tableau-based decision procedure for the full coalitional multiagent temporal-epistemic logic of linear time CMATEL(CD+LT). It extends LTL with operators of common and distributed knowledge for all coalitions of agents. The tableau procedure runs in exponential time, matching the lower bound obtained by Halpern and Vardi for a fragment of our logic, thus providing a complexity-optimal decision procedure for CMATEL(CD+LT).

cs.LO↗

arXiv2019

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.

math.LO↗

arXiv2019

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

We develop game-theoretic semantics (GTS) for the fragment ATL+ of the full Alternating-time Temporal Logic ATL*, essentially extending a recently introduced GTS for ATL. We first show that the new game-theoretic semantics is equivalent to the standard semantics of ATL+ (based on perfect recall strategies). We then provide an analysis, based on the new semantics, of the memory and time resources needed for model checking ATL+. Based on that, we establish that strategies that use only a very limited amount of memory suffice for ATL+. Furthermore, using the GTS we provide a new algorithm for model checking of ATL+ and identify a natural hierarchy of tractable fragments of ATL+ that extend ATL.

math.LO↗

arXiv2017

Logics for Propositional Determinacy and Independence

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyze the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that L_D and L_I naturally resolve a range of interpretational problems that arise in D and I. We also obtain sound and complete axiomatizations for L_D and L_I.

math.LO↗

arXiv2017

A logic for temporal conditionals and a solution to the Sea Battle Puzzle

Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle's famous "Sea Battle Tomorrow" puzzle leads to a fatalistic conclusion: whether there will be a sea battle tomorrow or not, but that is necessarily the case now. We propose a branching-time logic LTC to formalise reasoning about temporal conditionals and provide that logic with adequate formal semantics. The logic LTC extends the Nexttime fragment of CTL*, with operators for model updates, restricting the domain to only future moments where antecedent is still possible to satisfy. We provide formal semantics for these operators that implements the restrictor interpretation of antecedents of temporalized conditionals, by suitably restricting the domain of discourse. As a motivating example, we demonstrate that a naturally formalised in our logic version of the `Sea Battle' argument renders it unsound, thereby providing a solution to the problem with fatalist conclusion that it entails, because its underlying reasoning per cases argument no longer applies when these cases are treated not as material implications but as temporal conditionals. On the technical side, we analyze the semantics of LTC and provide a series of reductions of LTC-formulae, first recursively eliminating the dynamic update operators and then the path quantifiers in such formulae. Using these reductions we obtain a sound and complete axiomatization for LTC, and reduce its decision problem to that of the modal logic KD.

cs.LO↗

arXiv2015

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.

cs.LO↗

arXiv2015

Secure aggregation of distributed information: How a team of agents can safely share secrets in front of a spy

We consider the generic problem of Secure Aggregation of Distributed Information (SADI), where several agents acting as a team have information distributed among them, modeled by means of a publicly known deck of cards distributed among the agents, so that each of them knows only her cards. The agents have to exchange and aggregate the information about how the cards are distributed among them by means of public announcements over insecure communication channels, intercepted by an adversary "eavesdropper", in such a way that the adversary does not learn who holds any of the cards. We present a combinatorial construction of protocols that provides a direct solution of a class of SADI problems and develop a technique of iterated reduction of SADI problems to smaller ones which are eventually solvable directly. We show that our methods provide a solution to a large class of SADI problems, including all SADI problems with sufficiently large size and sufficiently balanced card distributions.

cs.CR↗

arXiv2013

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.

cs.GT↗

arXiv2013

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.

cs.GT↗

arXiv2013

How to Be Both Rich and Happy: Combining Quantitative and Qualitative Strategic Reasoning about Multi-Player Games (Extended Abstract)

We propose a logical framework combining a game-theoretic study of abilities of agents to achieve quantitative objectives in multi-player games by optimizing payoffs or preferences on outcomes with a logical analysis of the abilities of players for achieving qualitative objectives of players, i.e., reaching or maintaining game states with desired properties. We enrich concurrent game models with payoffs for the normal form games associated with the states of the model and propose a quantitative extension of the logic ATL* enabling the combination of quantitative and qualitative reasoning.

cs.LO↗