Related papers: Graded Hoare Logic and its Categorical Semantics
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
Hoare's logic is an axiomatic system of proving programs correct, which has been extended to be a separation logic to reason about mutable heap structure. We develop the most fundamental logical structure of strongest postcondition of…
We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
Using the programming language Haskell, we introduce an implementation of propositional calculus, number theory, and a simple imperative language that can evaluate arithmetic and boolean expressions. Finally, we provide an implementation of…
We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its…
We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…
Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
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…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…