Search results for "Logical connective"
showing 2 items of 2 documents
On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators
2020
The Tsetlin Machine (TM) is a recent machine learning algorithm with several distinct properties, such as interpretability, simplicity, and hardware-friendliness. Although numerous empirical evaluations report on its performance, the mathematical analysis of its convergence is still open. In this article, we analyze the convergence of the TM with only one clause involved for classification. More specifically, we examine two basic logical operators, namely, the "IDENTITY"- and "NOT" operators. Our analysis reveals that the TM, with just one clause, can converge correctly to the intended logical operator, learning from training data over an infinite time horizon. Besides, it can capture arbit…
Logics and operators
2003
Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to theories of a logic C defines a class of abstract algebras. The members of the class are called Lindenbaum-Tarski algebras of the logic C. One may abstract from the origin of these algebras and exa…