Archimedes and double contradiction proof

Negation and Proof by Contradiction in Access-Limited Logic

Access-Limited Logic (ALL) is a language for knowledge representation which formalizes the access limitations inherent in a network structured knowledge-base. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an access-limited logic retrieves all assertions reachable by following an available access path. In this paper, we extend previous wo...

A PROOF OF FREEDOM FROM CONTRADICTION By ALONZO

Contradiction Detection with Contradiction-Specific Word Embedding

Contradiction detection is a task to recognize contradiction relations between a pair of sentences. Despite the effectiveness of traditional context-based word embedding learning algorithms in many natural language processing tasks, such algorithms are not powerful enough for contradiction detection. Contrasting words such as “overfull” and “empty” are mostly mapped into close vectors in such e...

Conjunction and Contradiction

The Law of Non-Contradiction (hereafter: LNC) says that no contradiction can be true. But what is a contradiction? And what does it take for a contradiction to be true? As Patrick Grim [5] has pointed out, a quick look at the literature will reveal a large menagerie of different interpretations of the basic terms and, consequently, of LNC. Grim actually identifies as many as 240 different optio...

Self-Contradiction and Contradiction between Two Atanassov's Intuitionistic Fuzzy Sets

The paper focuses on the study of the contradiction between two Atanassov's intuitionistic fuzzy sets. First, taking into account some characterizations obtained in previous papers, some functions are defined in order to measure the degrees of contradiction. Besides the principal properties of these measures are pointed out. Finally, some results relating self-contradiction and contradiction be...