A Survey of Satisfiability Modulo Theory

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches. We also cover quantifiers, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. 201

Synthesising and Implementing Tableau Calculi for Interrogative Epistemic Logics

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.

Achieving while maintaining:A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $\phi$ given $\psi$ while maintaining $\chi$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.Comment: appear in Proceedings of ICLA 201

Tableaux for the Logic of Strategically Knowing How

The logic of goal-directed knowing-how extends the standard epistemic logic with an operator of knowing-how. The knowing-how operator is interpreted as that there exists a strategy such that the agent knows that the strategy can make sure that p. This paper presents a tableau procedure for the multi-agent version of the logic of strategically knowing-how and shows the soundness and completeness of this tableau procedure. This paper also shows that the satisfiability problem of the logic can be decided in PSPACE.Comment: In Proceedings TARK 2023, arXiv:2307.0400