Abstract Guarded Kleene Algebra with Tests (GKAT) was presented as a fragment of KAT to abstract imperative programming languages, where only if-then-else and while-do statements are allowed in the language. The loss of expressiveness is, nevertheless, compensated by a clear advantage over KAT: it allows almost linear decidability of program equivalence. In this work, we give the first step to optimizing the complexity of dynamic logic equivalence, which is EXPTIME-complete in propositional dynamic logic (PDL). First, and based on strict deterministic PDL, we present guarded propositional dynamic logic (GPDL), a fragment of PDL where programs correspond to GKAT terms. It comes embedded, as expected, with a semantics over relational models and a sound axiomatisation. Then, we present a Natural Deduction system for GPDL, proving its soundness and completeness, concerning the axiomatisation. Based on Smolka et al. (2019, Proceedings of the ACM Programming Language 4), we obtain the main result of this work—the equivalence of GPDL programs can be established in almost linear time.

Abstract This paper introduces two logic frameworks for the study of SIR (Susceptible-Infected-Recovered) and SIRS compartmental epidemic models, one based on Linear Temporal Logic and the other on Computation Tree Logic. We provide a short literature overview on compartmental models and other related works using logics, and then define our logics with their respective axiomatizations, and demonstrate their soundness and completeness proofs.

Abstract This paper introduces a logic with a class of social network models that is based on standard Linear Temporal Logic, which allows for leveraging the power of existing model checkers for the analysis of social networks. We provide a short literature overview, and then define our logic and its axiomatization, present some simple motivational examples of both models and formulas and show its soundness and completeness via a translation into propositional formulas. Lastly, we discuss model checking, time complexity analysis and a Susceptible–Infectious–Recovered model variation for infectious diseases.

This work presents three increasingly expressive Dynamic Logics in which the programs are described in a language based on CCS. Our goal is to build dynamic logics that are suitable for the description and verification of properties of communicating concurrent systems, in a similar way as PDL is used for the sequential case. In order to accomplish that, CCS’s operators and constructions are added to a basic modal logic. Doing this, the semantics of CCS’s parallel operator allows us to build dynamic logics that support communicating and concurrent programs. We build a simple Kripke semantics for these logics, provide complete axiomatizations for them and show that they have the finite model property. This contrasts with other dynamic logics with parallel operators presented in the literature, such as Peleg’s Concurrent PDL with Channels, where either the parallel programs cannot communicate, or at least one of the properties mentioned above (simple Kripke semantics, complete axiomatization and finite model property) is missing.

This work provides a constructive presentation of modal logis in natural deduction style. The modal connective □ is presented in a constructive form, which can be considered as an operational semantics for it. Modal connectives have been recognized as intentional connectives for a long time, but modal logicians have insisted in using extensional techniques to deal with them. In this paper, the modal connective is presented as a higher-order connective defined on top of the object level logical connectives. The simplest version of our system of modal logic with classical negation coincides with the classical modal logic K. The most important modal logics have an elegant presentation in this system. T, S4, S5, D, D4, D5 are presented, without any side effect condition on the structure of the deductions. Most presentations of intuitionistic modal logics fail in giving an intuitionistic interpretation to the modal connective. In general, such interpretations are based on some alien element (for instance, the accessibility relation), which are by no means intuitionistic. In the system described here it is not only possible to present an intuitionistic interpretation of the modal connective □, which takes into account only deducibility issues, but also to give a constructive natural deduction presentation for the □.