相关论文: Algorithmic correspondence and completeness in mod…

The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must…

We report on work in progress on automatic procedures for proving properties of programs written in higher-order functional languages. Our approach encodes higher-order programs directly as first-order SMT problems over Horn clauses. It is…

Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…

We formalize a multivariate quantifier elimination (QE) algorithm in the theorem prover Isabelle/HOL. Our algorithm is complete, in that it is able to reduce any quantified formula in the first-order logic of real arithmetic to a logically…

We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and…

We introduce an efficient algorithmic procedure for implementing the direct formula that represents the product of splines in the B-spline basis. We first demonstrate the relevance of this direct approach through numerical evidence showing…

We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…

Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In…

This paper develops stable canonical rules for intuitionistic modal logics, which were first introduced for superintuitionistic logics and transitive nor mal modal logics in [1] and [2] respectively. We first prove that every in…

We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…

We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia…

The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…

Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of…

Recent published work has addressed the Shalqvist correspondence problem for non-distributive logics. The natural question that arises is to identify the fragment of first-order logic that corresponds to logics without distribution, lifting…

Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…