We present AKR , a model checking tool for an adaptative probabilistic knowing-how epistemic logic. The tool takes as input the specification of a scenario modeled via a probabilistic LTS (in PRISM notation), a collection of regular expressions acting as agent’s perception, a knowing-how property, and checks whether the formula holds in the model under the given perception. The tool combines automata-based techniques with calls to the PRISM tool to compute the result. AKR is a publicly available, open-source tool entirely programmed in Python . We describe the tool’s architecture and illustrate its use via some examples.

Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning tools. More recently, it has been shown that the expressive power provided by the operators characterizing Hybrid Logics (nominals and satisfiability modalities) can be used to internalize labels, leading to well-behaved inference procedures for fairly expressive logics. The resulting procedures are attractive because they do not use external mechanisms outside the language of the logic at hand, and have good logical and computational properties. Many tableau systems based on Hybrid Logic have been investigated, with more recent efforts concentrating on Modal Logics that support data comparison operators. Here, we introduce an internalized tableau calculus for XPath, arguably one of the most prominent approaches for querying semistructured data. More precisely, we define data-aware tableaux for XPath featuring data comparison operators and enriched with nominals and the satisfiability modalities from Hybrid Logic. We prove that the calculus is sound, complete and terminating. Moreover, we show that tableaux can be explored in polynomial space, therefore establishing that the satisfiability problem for the logic is PSpace-complete. Finally, we explore different extensions of the calculus, in particular how to handle data trees and other frame classes.

Abstract We report on an implementation of a tableaux calculus for sceptical consequence in Default Logic built on Hybrid Modal Logic. In turn, our tool offers support for checking default consequence over formulas from Propositional Logic, Basic Modal Logic and Hybrid Logic. We develop a test suite for assessing the correctness, scalability, and efficiency of our system, and inform on the results. Interestingly, our method can be adapted to generate examples for other default provers.

Abstract Default Logics are a family of non-monotonic formalisms having so-called defaults and extensions as their common foundation. Traditionally, default logics have been defined and dealt with via syntactic notions of consequence in propositional or first-order logic. Here, we build default logics on modal logics. First, we present these default logics syntactically. Then, we elaborate on an algebraic counterpart. More precisely, we extend the notion of a modal algebra to accommodate for defaults and extensions. Our algebraic view of default logics concludes with an algebraic completeness result and a way of comparing default logics borrowing ideas from the concept of bisimulation in modal logic. To our knowledge, this take on default logics approach is novel. Interestingly, it also lays the groundwork for studying default logics from a dynamic logic perspective.

In this paper we introduce a prioritized default logic. We build this logic modularly from Standard Deontic Logic by the addition of default rules and priorities among them. Our main aim is to provide a logical framework to reason about scenarios where prescriptive and descriptive statements coexist and may be incomplete and contradictory. We motivate and illustrate the technical elements of our work with the use of examples (classical, and coming from software engineering). In addition, we present sound, complete, and terminating (with loop check) tableau-based proof calculi for credulous and sceptical reasoning in our logic.