Multi-agent Logics with Interacting Agents Based on Linear Temporal Logic: Deciding Algorithms

Abstract

We introduce a multi-agent logic \({ {\cal M}{\cal A}_{{\cal L}{\cal T}{\cal L}}}\) – a variant of the linear temporal logic LTL with embedded multi-agent knowledge with interacting agents. The logic is motivated by semantics based on potentially infinite runs with time points represented by clusters of states with distributed knowledge of the agents. We address properties of local and global knowledge modeled in this framework, consider modeling of interaction between agents by possibility to puss information from one agent to others via possible transitions within time clusters of states. Main question we are focused on is the satisfiability problem and decidability of the logic \({ {\cal M}{\cal A}_{{\cal L}{\cal T}{\cal L}}}\). Key result is proposed algorithm which recognizes theorems of \({ {\cal M}{\cal A}_{{\cal L}{\cal T}{\cal L}}}\) (so we show that \({ {\cal M}{\cal A}_{{\cal L}{\cal T}{\cal L}}}\) is decidable). It is based on verification of validity for special normal reduced forms of rules in models with at most triple exponential size in the testing rules. In the final part we discuss possible variations of the proposed logic.Keywordsmulti-agent logichybrid logicsknowledge based reasoningrelational Kripke/Hintikka modelsdecidability algorithms