Carlos Olarte

We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each logic, where necessitation is captured by the systematic use of level valuations. The semantics is grounded in an eight-valued system and provides a sound and complete decision procedure for each modal logic, extending and refining earlier semantics as particular cases. Additionally, we propose a novel model-theoretic perspective that links our framework to relational (Kripke-style) semantics, addressing longstanding questions regarding the correspondence between modal axioms and semantic conditions in non-deterministic settings. This yields a philosophically robust and technically modular alternative to traditional possible-world semantics.

This paper introduces a generalised opinion model that extends the standard DeGroot model by representing agents' opinions and influences as soft constraints rather than single real values. This allows for modelling scenarios beyond the scope of the DeGroot model, such as agents sharing partial information and preferences, engaging in discussions on multiple topics simultaneously, and representing opinions with different degrees of uncertainty. By considering soft constraints as influences, the proposed model captures also situations where agents impose conditions on how others' opinions are integrated during belief revision. Finally, the flexibility offered by soft constraints allows us to introduce a novel polarisation measure that takes advantage of this generalised framework.

Strategic Timed CTL (STCTL) is an expressive logic that integrates branching time CTL with the representation of continuous time, and the notion of strategic abilities of agents. This makes STCTL suitable for specifying properties of asynchronous multi-agent systems modeled as networks of Parametric Timed Automata (PTA). Existing model checkers and synthesis procedures for STCTL are often limited in scope (bounded analyses), rely on ad-hoc implementations, and are difficult to prove correct. In this paper we propose declarative methods for STCTL model checking and synthesis using rewriting logic. Our approach uses rewriting modulo SMT to represent clock constraints and timed parameters as terms in a rewrite theory, and we adequately capture the continuous semantics of STCTL via rewriting strategies. The resulting algebraic specification is executable in the rewrite engine Maude. This is a novel application of Maude’s strategy language and, since our procedures are grounded on logical means, it is simpler to prove them correct. Our approach advances the state of the art for the analysis of multi-agent systems by allowing for the nesting of temporal operators and universal STCTL formulas, which have not been considered before. We benchmark our rewrite theory against existing procedures for STCTL, demonstrating competitive performance and even outperforming dedicated procedures for the existential fragment of STCTL. We thus provide a more robust and verifiable approach to STCTL model checking and synthesis.