Related papers: Object-Oriented Theorem Proving (OOTP): First Thou…
A unit test is a method for verifying the accuracy and the proper functioning of a portion of a program. This work consists to study the relation and the approaches to test Object-Oriented Programming (OOP) programs and to propose a…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
We introduce a new framework to evaluate and improve first-order (FO) ontologies using automated theorem provers (ATPs) on the basis of competency questions (CQs). Our framework includes both the adaptation of a methodology for evaluating…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, leading to their adoption in high-stakes domains such as healthcare, law, and scientific research. However, their reasoning often contains subtle logical…
The MTP is an emerging standard for the software integration of process modules into a control system. The core concept of MTP is to separate process plants into autonomous modules called PEA which offer easy to use high level services.…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
The paper introduces the principles of object-oriented translation for target machine which provides executing the sequences of elementary operations on persistent data presented as a set of relations (programmable relational system). The…
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…
The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. We define a fixed point logic (FPL) extension of Clark's completion such that…
Property-based testing (PBT) is a technique for validating code against an executable specification by automatically generating test-data. We present a proof-theoretical reconstruction of this style of testing for relational specifications…
Background: Aspect-oriented programming (AOP) is an emerging programming paradigm whose focus is about improving modularity, with an emphasis on the modularization of crosscutting concerns. Objective: The goal of this paper is to assess the…
The paper tackles the issue of mapping logic axioms formalised in the Ontology Web Language (OWL) within the Object-Oriented Programming (OOP) paradigm. The issues of mapping OWL axioms hierarchies and OOP objects hierarchies are due to…