Related papers: Mechanised uniform interpolation for modal logics …

Using Isabelle/HOL, we verify a union-find data structure with an explain operation due to Nieuwenhuis and Oliveras. We devise a simpler, more naive version of the explain operation whose soundness and completeness is easy to verify. Then,…

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…

Using differential techniques, we compute the Jacquet module of the locally analytic vectors of irreducible admissible unitary representations of GL_2(\qp). This gives a direct proof of some results of Colmez, leading to a proof of…

This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…

We introduce k-quantifier logics -- logics with access to k-tuples of elements and very general quantification patterns for transitions between k-tuples. The framework is very expressive and encompasses e.g. the k-variable fragments of…

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties…

We suggest a formalism to illustrate the entanglement of identical particles in the first quantization language (1QL). Our 1QL formalism enables one to exploit all the well-established quantum information tools to understand the…

We combine quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with temporal logic for reasoning about the temporal behavior during their operation. Our logic supports…

Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, equality is appallingly syntactic and, as a result, exploiting equivalences is cumbersome at best.…

Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…

There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

We present the linear first-order intermediate language IL for verified compilers. IL is a functional language with calls to a nondeterministic environment. We give IL terms a second, imperative semantic interpretation and obtain a register…

Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…

This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.

This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation. We focus on showing…

Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated…

We compute the equivariant $KO$-homology of the classifying space for proper actions of $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. We also compute the Bredon homology and equivariant $K$-homology of the classifying spaces…