Since at least the early 1980s there has been an effort to utilize multiple processors for logical reasoning. Prior to the rise of the multi-core desktop computer, this often meant parallel algorithms on specialized hardware. Parallel logic programming systems designed during that same period were less attached to a particular parallel architecture, but parallelizing Prolog is a very complex pr...

The logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details to our conceptual knowledge. In this paper, we will look into how this reasoning techniquesabduction, deduction and induction, are relevant in neural networks logic programming. Deduction simplifies the knowledge representation without affecting...

A logical space is a pair of a non-empty set and a subset of , and a deduction pair on is a pair of a subset of and a relation between ∗ and . It will be shown that we can understand the true nature of logical completeness via consideration of those simple notions.

The Mizar project is a long-term eeort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system developed by Ja skowski. The texts written in the language are called Mizar articles and are organiz...

Derivations and proofs are a form of provenance in automated deduction that can assist users in understanding how reasoners derive logical consequences from premises. However, system-generated proofs are often overly complex or detailed, and making sense of them is non-trivial. Conversely, without any form of provenance, it is just as hard to know why a certain fact was derived. We study proven...

According to current psychological models of deduction, people can draw inferences on the basis of information that they receive from different sources at different times. In 3 reading-comprehension experiments, the authors demonstrated that premises that appear far apart in a text (distant) are not accessed and are therefore not used as a basis for logical inferences (Experiment 1), unless the...

Formal verification (FV) involves the use of logical reasoning to establish properties of a computer program (or hardware element, protocol etc.) In the purest form of FV, rigorous logical deduction is used to prove with full mathematical rigor that the program satisfies a logical specification. This is often contrasted with the traditional approach of testing on a variety of specific inputs or...

This paper presents a graph-based knowledge representation and reasoning language. This language benefits from an important syntactic operation, which is called a graph homomorphism. This operation is sound and complete with respect to logical deduction. Hence, it is possible to do logical reasoning without using the language of logic but only graphical, thus visual, notions. This paper present...

In the School of Mathematical Sciences at Queen Mary in the University of London we have been running a module that teaches the students to write good mathematical English. The module is for second-year undergraduates and has been running for three years. It is based on logic, but the logic—though mathematically precise—is informal and doesn’t use logical symbols. Some theory of definitions is ...

The problem of Information Retrieval is, given a set of documents D and a query q, providing an algorithm for retrieving all documents in D relevant to q. However, retrieval should depend and be updated whenever the user is able to provide as an input a preferred set of relevant documents; this process is known as relevance feedback. Recent work in IR has been paying great attention to models w...