Synthesising and Implementing Tableau Calculi for Interrogative Epistemic Logics

Abstract

This paper presents a labelled tableau approach for deciding interrogative-epistemic logics (IEL). Tableau calculi for these logics have been derived using a recently introduced tableau synthesis method. We also consider an extension of the framework for a setting with questioning modalities over sequences of formulae called sequential questioning logic (SQL). We have implemented the calculi using two approaches. The first implementation has been obtained with the tableau prover generation software MetTeL 2 , while the other implementation is a prover implemented in Haskell.

RAESON: A Tool for Reasoning Tasks Driven by Interactive Visualization of Logical Structure

“…These decomposition rules are based on applying metanominals to possible worlds as Skolem terms constructed from formulae containing modal operators and using relational properties of accessible successors during tableau expansion. The theoretical background behind this technique has been described in full detail in [6], and the logical grammar used for parsing hybrid logic formulae in the specification metalanguage is also included for reference in Section 7. Concrete teaching context are included in Sections 4, 5.…”

“…In the previous use case scenario you have found a counterexample to a formula labeled as an axiom, now you are going to fix this. If needed, go through steps (1)(2)(3)(4)(5)(6) in the previous use case to obtain the open tableau and the countermodel illustrated in Figure 2 (middle, respectively, right). Step (7): Click on the Copy to Sandbox Library feature.…”

“…The logic specific application component consists of several modules containing functionality handling formal aspects concerning the syntax and semantics of the logics and dealing with their associated reasoning tasks. These include a term unification package and an expression parser [12], a module for translating syntax into D3 tree layout, a tableau based theorem prover [6] with a corresponding module to translate the analytic tableau proof trace into a D3 force graph layout with a hierarchical tree structure, and a (counter)model generator [7] with a corresponding module for translating the (closed) tableau branches into (counter)example relational structures and further into a D3 force graph layout.…”

MetTeL²: Towards a Tableau Prover Generation Platform

“…This is particularly pertinent to an area such as multi-agent systems where the logics are staggering complex. In ongoing work we are using MetTeL 2 in combination with the tableau synthesis framework to develop provers for multi-agent interrogative epistemic logics [21]. For these logics and related dynamic epistemic logics there are almost no implemented reasoning tools.…”

“…Concrete case studies we have undertaken with MetTeL 2 include implementing unlabelled tableau calculi for Boolean logic and three-valued Lukasiewicz logic, labelled tableau calculi for standard modal logics K, KT, S4, description logic ALCO, a hybrid logic K(E n ) with global counting operators [19], a multi-agent interrogative epistemic logic [21], and internalised tableau calculi for hybrid and description logics. We used MetTeL 2 to implement a tableau decision procedure for ALBO id , a description logic with the same expressive power as the two-variable fragment of first-order logic.…”