Multi-agent Logic Research Articles

Synergistic knowledge

Simplicial complexes are a successful model for distributed computing. They have recently been observed to provide an interesting model for epistemic multi-agent logic where the agents' local states are the main building blocks (instead of the global states). A natural generalization is to study epistemic logic on semi-simplicial sets. However, finding the appropriate modal logic for semi-simplicial models has been an open question. We answer this by introducing the logic of synergistic knowledge and establishing its soundness and completeness.

Complexity results for modal logic with recursion via translations and tableaux

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics via translations to and from the $\mu$-calculus and modal logic, which allow us to transfer known upper and lower bounds. We also use these translations to introduce terminating and non-terminating tableau systems for the logics we study, based on Kozen's tableau for the $\mu$-calculus and the one of Fitting and Massacci for modal logic. Finally, we describe these tableaux with $\mu$-calculus formulas, thus reducing the satisfiability of each of these logics to the satisfiability of the $\mu$-calculus, resulting in a general 2EXP upper bound for satisfiability testing.

Dynamic Temporal Logical Operations in Multi-Agent Logics

Dynamic Temporal Logical Operations in Multi-Agent Logics

Complexity through Translations for Modal Logic with Recursion

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics via translations to and from the mu-calculus and modal logic, which allow us to transfer known upper and lower bounds. We also use these translations to introduce a terminating tableau system for the logics we study, based on Kozen's tableau for the mu-calculus, and the one of Fitting and Massacci for modal logic.

Unification and Finite Model Property for Linear Step-Like Temporal Multi-Agent Logic with the Universal Modality

This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality \(\mathcal{LTK}.sl_U\) based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic.

A computationally grounded logic of awareness

Abstract We introduce a multi-agent logic of explicit, implicit belief and awareness with a semantics using belief bases. The novelty of our approach is that an agent’s awareness is not a primitive but is directly computed from the agent’s belief base. We prove soundness and completeness of the logic relative to the belief base semantics. Furthermore, we provide a polynomial embedding of the logic of propositional awareness into it and a polynomial embedding of our logic into the logic of general awareness. Thanks to the latter embedding, we show that the satisfiability checking problem for our logic is PSPACE complete. Finally, we extend it by the notions of public announcement and private belief expansion.

Multi-Agent Logics with Dynamic Accessibly Relations, Projective Unifiers

Multi-Agent Logics with Dynamic Accessibly Relations, Projective Unifiers

Temporal Multi-Agents’ Logics Modelling Dynamic Temporal Accessibility Relations

Here we continue our research connected with multi-agent logics and theirs applications to Information Sciences. We work with multi-agent logics based at relational models where time accessibility relations are not compulsory transitive and not compulsory are solid or continuous. We admit that time accessibility relations may have gaps or places of forgotten time. Several various approaches to formalizations paths of accessibility by time are suggested. Among them the case when each time state generates its own time - an interval of time which states are accepted as all the time accessible for any given agent in that time state. Variation of this approach when an external modelling initially introduced as all the times forgotten for the agent and not accessible for this agent at all. Also we study the case with time sates imitated as clusters of information states for current time. Examples of representation important properties concerning knowledge and information via logical formulas are provided. Mathematical results are formulated in terms of decidability and satisfiability problem, and existence of corresponding algorithms are stated. Open problems are suggested in the conclusion.

A Multi-Agent Spatial Logic for Scenario-Based Decision Modeling and Verification in Platoon Systems

A Multi-Agent Spatial Logic for Scenario-Based Decision Modeling and Verification in Platoon Systems

A survey of requirements for COVID-19 mitigation strategies

The COVID-19 pandemic has influenced virtually all aspects of our lives. Across the world, countries have applied various mitigation strategies, based on social, political, and technological instruments. We postulate that multi-agent systems can provide a common platform to study (and balance) their essential properties. We also show how to obtain a comprehensive list of the properties by “distilling” them from media snippets. Finally, we present a preliminary take on their formal specification, using ideas from multi-agent logics. © 2021 The Author(s).

A Model for Verification and Validation of Law Compliance of Smart Contracts in IoT Environment

The interest of Industry 4.0 in smart contracts and blockchain technologies is growing up day by day. Smart contracts have enabled new kinds of interactions whereby contractors can even fully automate processes they agree on. This technology is really appealing in Internet of Things (IoT) domain because smart devices generate events for software agents involved in a smart contract execution, making full automation possible. However, smart contracts have to comply with national and international laws and accountability of participant's actions. Soundness of a smart contract has to be verified in terms of law compliance. Here, we propose a model for verification and validation of law compliance of smart contracts in IoT environments. The main goal of this article is to propose a formal model (based on multiagent logic and ontological description of contracts) for validating law compliance of smart contracts and to determine potential responsibilities of failures.

A Non-alethic Multi-agent Doxastic Logic as a Solution to Epistemic Conflicts

The non-alethic systems N1 of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic NADK can be obtained by logical expansion. The soundness and completeness of NADK are proved and its special theorems are also presented. In this logic, the belief version of the laws of contradiction and excluded middle, as well as the principle of explosion are all invalid. Therefore, it may provide a reliable logical basis for any theory which has paraconsistent or paracomplete epistemic conflicts, such as true contradictions, true contrarieties, and belief paradoxes. We also explain in detail how a non-alethic doxastic logic provides a reliable logical basis for tolerating these three types of epistemic conflicts. The present paper is the deepening and development of system N1 and A.

Pragmatic Distance in IoT Devices

Stand-alone devices perform their functions without human intervention. These types of devices would benefit from capabilities that allow collaboration among the devices in order to maximize service availability, as well as dynamic adaptation of the devices to user requirements in order to minimize resource usage. For example, when detecting a malfunction in one of the devices, the system should find devices with similar functionality to recover the overall service by functionality substitution. Additionally, for example, in the context of a user with hearing loss, the system should utilize devices with visual feedback functionality and disable audio feedback functionality to conserve resources. In this paper, we describe the implementation of a method to detect similar functionalities between heterogeneous devices, denoted Lightweight Machine to Machine Resource Pragmatic Distance (LwRPD). We define that devices are pragmatically close if they can be substituted with each other in order to perform a specific function in a particular context. We implement the method for enabling the aforementioned capabilities in specific use cases, using resources from real-life devices, to demonstrate the benefits. We also compare LwRPD with a multi-agent pragmatic similarity metric, Fuzzy logic and Levenshtein distance techniques, demonstrating LwRPD superiority over those techniques.

Multi-agent temporal nontransitive linear logics and the admissibility problem

We study an extension of temporal logic, a multi-agent logic on models with nontransitive linear time (which is, in a sense, also an extension of interval logic). The proposed relational models admit lacunas in admissibility relations among agents: information accessible for one agent may be inaccessible for others. A logical language uses temporary operators ‘until’ and ‘next’ (for each of the agents), via which we can introduce modal operations ‘possible’ and ‘necessary.’ The main problem under study for the logic introduced is the recognition problem for admissibility of inference rules. Previously, this problem was dealt with for a logic in which transitivity intervals have a fixed uniform length. Here the uniformity of length is not assumed, and the logic is extended by individual temporal operators for different agents. An algorithm is found which decides the admissibility problem in a given logic, i.e., it recognizes admissible inference rules.

Multi-Agent Temporal Nontransitive Linear Logics and the Admissibility Problem

We study an extension of temporal logic, a multi-agent logic on models with nontransitive linear time (which is, in a sense, also an extension of interval logic). The proposed relational models admit lacunas in admissibility relations among agents: information accessible for one agent may be inaccessible for others. A logical language uses temporary operators ‘until’ and ‘next’ (for each of the agents), via which we can introduce modal operations ‘possible’ and ‘necessary.’ The main problem under study for the logic introduced is the recognition problem for admissibility of inference rules. Previously, this problem was dealt with for a logic in which transitivity intervals have a fixed uniform length. Here the uniformity of length is not assumed, and the logic is extended by individual temporal operators for different agents. An algorithm is found which decides the admissibility problem in a given logic, i.e., it recognizes admissible inference rules.

Multi-Agent Logics with Multi-Valuations and Intensional Logical Operations

We consider a multi-agent logic based on linear temporal logic. This logic uses as the semantics relational temporal models with multi-valuations—the models have separate valuations for all agents. We introduce in the logical language two new intensional logical operations—plausible and dominates—to capture the feature of uncertainty. The main mathematical problem we are dealing with is the satisfiability problem. We solve it and find deciding algorithm. In the final part of paper we discuss interesting open problems for possible further investigations.

Representation of Information and Satisfiability, Algorithms for Multi-Agent Logics

This paper studies logical properties of multi-agent logics based at relational models with elements of multi-agency. In particular, we introduce a multi-agent temporal logic PastL based at linear possible-worlds models with non-transitive and non-uniform accessibility relations. We consider the time directed to past, and use logical operation Since for non-transitive accessibility; Several formalizations for the conception knowledge/agent’s knowledge in terms of non-transitive time in past are suggested. A logics PastT based is this approach is studied, we consider main computational problems - satisfiability and decidability. Based at technique of reduced normal forms we solve these problems and find deciding algorithms. Several interesting open problems are suggested. In final part of the paper we extend obtained results on logics with different accessibility relations for different agents and consider the satisfiability problem for these logics.

Multi-Agent Logic’s Modelling Non-Monotonic Information and Reasoning

Abstract We study multi-agent logic modelling non-monotonic reasoning and taking decisions. Non-monotonicity is reflected by means of non-transitive agents’ accessibility relations. The semantics is based at relational models for modelling computational processes and analysis of databases with incomplete information, for instance, with information forgotten in the past. Besides, the agents’ accessibility relations may have lacunas; agents may have no access to some potentially known and stored information. Satisfiability and decidability issues are discussed. We find algorithms solving satisfiability problem. Illustrating examples are provided.

Multi-agent Logics for Reasoning About Higher-Order Upper and Lower Probabilities

We present a propositional and a first-order logic for reasoning about higher-order upper and lower probabilities. We provide sound and complete axiomatizations for the logics and we prove decidability in the propositional case. Furthermore, we show that the introduced logics generalize some existing probability logics.

Disjunctive Normal Form for Multi-Agent Modal Logics Based on Logical Separability

Modal logics are primary formalisms for multi-agent systems but major reasoning tasks in such logics are intractable, which impedes applications of multi-agent modal logics such as automatic planning. One technique of tackling the intractability is to identify a fragment called a normal form of multiagent logics such that it is expressive but tractable for reasoning tasks such as entailment checking, bounded conjunction transformation and forgetting. For instance, DNF of propositional logic is tractable for these reasoning tasks. In this paper, we first introduce a notion of logical separability and then define a novel disjunctive normal form SDNF for the multiagent logic Kn, which overcomes some shortcomings of existing approaches. In particular, we show that every modal formula in Kn can be equivalently casted as a formula in SDNF, major reasoning tasks tractable in propositional DNF are also tractable in SDNF, and moreover, formulas in SDNF enjoy the property of logical separability. To demonstrate the usefulness of our approach, we apply SDNF in multi-agent epistemic planning. Finally, we extend these results to three more complex multi-agent logics Dn, K45n and KD45n.