Abstract We present an Isabelle/HOL formalization of Simple Clause Learning for first-order logic without equality: SCL(FOL). The main results are formal proofs soundness, non-redundancy learned clauses, termination, and refutational completeness. Compared to the unformalized version, formalized calculus is simpler more general, some such as stronger non-subsumption new. found one bug in a prev...

There are still very few systems performing a Similarity Based Learning and using a First Order Logic (FOL) representation. This limitation comes from the intrinsic complexity of the learning processes in FOL and from the difficulty to deal with numerical knowledge in this representation. In this paper, we show that major learning processes, namely generalization and clustering, can be solved i...

In this paper, we present the FOLtoNL system, which converts first order logic (FOL) sentences into natural language (NL) ones. The motivation comes from an intelligent tutoring system teaching logic as a knowledge representation language, where we use it as a means for feedback to the users. FOL to NL conversion is achieved by using a rule-based approach, where we exploit the pattern matching ...

A number of Inductive Logic Programming (ILP) systems have addressed the problem of learning First Order Logic (FOL) discriminant definitions by first reformulating the FOL learning problem into an attribute-value one and then applying efficient learning techniques dedicated to this simpler formalism. The complexity of such propositionalisation methods is now in the size of the reformulated pro...

There are still very few systems performing a Similarity Based Learning and using a First Order Logic (FOL) representation. This limitation comes from the intrinsic complexity of the learning processes in FOL and from the difficulty to deal with numerical knowledge in this representation. In this paper, we show that major learning processes, namely generalization and clustering, can be solved i...

Knowledge Representation & Reasoning (KR&R) is a fundamental topic in Artificial Intelligence. A basic KR language is First– Order Logic (FOL), the most representative logic–based representation language, which is part of almost any introductory AI course. In this work we present KRRT (Knowledge Representation & Reasoning Tutor). KRRT is a Web–based system which main goal is to help the student...

First-order logic (FOL) is undecidable — that is, no algorithm exists that can decide whether a formula of FOL is valid or not. However, there are various fragments of FOL that are known to be decidable. FO, the two-variable fragment of FOL, is one of such languages [1, 2]. FO is a first-order language where formulas have maximally two variables, no function symbols, but possibly do have equali...

Fusarium oxysporum is a soil-born fungus that induces wilt and root rot on a variety of plants. F. oxysporum f. sp. conglutinans (Foc) can cause wilt disease on cabbage. This study showed that a homolog of SIX1 protein in the Arabidopsis infecting isolate Fo5176 (Fo5176-SIX1) had four isoforms in the conidia of Foc by proteomic analysis. Thus, we analyzed the roles of protein Foc-SIX1. Gene exp...

We wish to improve modeling in first-order logic (FOL) by using object-oriented tools. To this end, we describe Object-Oriented First-Order Logic (OOFOL), which is a simple extension of FOL. It does not surpass the expressive power of FOL, but it provides object-oriented tools to the knowledge engineer. In OOFOL, objects are theories that are connected via interface vocabularies to other object...

Since gene expression approaches constitute a starting point for investigating plant-pathogen systems, we performed a transcriptional analysis to identify a set of genes of interest in tomato plants infected with F. oxysporum f. sp. lycopersici (Fol) and Tomato Mosaic Virus (ToMV). Differentially expressed tomato genes upon inoculation with Fol and ToMV were identified at two days post-inoculat...