Related papers: Algorithmic correspondence and completeness in mod…
Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
We introduce the algorithm MASSA which takes classical modal formulas in input, and, when successful, effectively generates: (a) (analytic) geometric rules of the labelled calculus G3K, and (b) cut-free derivations (of a certain `canonical'…
Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
First-order model counting emerged recently as a novel reasoning task, at the core of efficient algorithms for probabilistic logics. We present a Skolemization algorithm for model counting problems that eliminates existential quantifiers…
Fine's influential Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result,…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
Modal logic with propositional quantifiers (i.e. second-order propositional modal logic (SOPML)) has been considered since the early time of modal logic. Its expressive power and complexity are high, and its van-Benthem-Rosen theorem and…
We extend unified correspondence theory to Kripke frames with impossible worlds and their associated regular modal logics. These are logics the modal connectives of which are not required to be normal: only the weaker properties of…
Skolemization, with Herbrand's theorem, underpins automated theorem proving and various transformations in computer science and mathematics. Skolemization removes strong quantifiers by introducing new function symbols, enabling efficient…
The continuous modal mu-calculus is a fragment of the modal mu-calculus, where the application of fixpoint operators is restricted to formulas whose functional interpretation is Scott-continuous, rather than merely monotone. By…
The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial…
In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form $\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_\lambda x_j$. We prove that many properties of these logics, such…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
By exploiting the algebraic and order theoretic mechanisms behind Sahlqvist correspondence, the theory of unified correspondence provides powerful tools for correspondence and canonicity across different semantics and signatures, covering…
The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist…
Sabotage modal logic (SML) is a kind of dynamic logics. It extends static modal logic with a dynamic modality which is interpreted as "after deleting an arrow in the frame, the formula is true". In the present paper, we are aiming at…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have…
We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and…
The present paper establishes systematic connections among the first-order correspondents of Sahlqvist modal reduction principles in various relational semantic settings which include crisp and many-valued Kripke frames, and crisp and…