相关论文: Formulas as Programs

This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

In a recent paper by Harrison et al., the concept of program completion is extended to a large class of programs in the input language of the ASP grounder gringo. We would like to automate the process of generating and simplifying…

We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…

We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…

In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of…

Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the…

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this…

It is discussed a practical possibility of a provable programming of mathematics basing on intuitionism and the dependent types feature of a programming language.The principles of constructive mathematics and provable programming are…

Some approaches to increasing program reliability involve a disciplined use of programming languages so as to minimise the hazards introduced by error-prone features. This is realised by writing code that is constrained to a subset of the a…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a…

If code is law, then the language of law is a programming language. Lawyers and legal scholars can learn about law by studying programming-language theory, and programming-language tools can be usefully applied to legal problems. This…

We present a semi-automated framework to construct and reason about programs in a deeply-embedded while-language. The while-language we consider is a simple computation model that can simulate (and be simulated by) Turing Machines with a…

The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…

An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…

We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…