We derive solution-formulae for the Krichever–Novikov equation by a systematic multipotentialisation of equation. The formulae are achieved due to connections equations certain symmetry-integrable 3rd-order evolution which admit autopotentialisations.

When dealing with a situation in which new information is to be incorporated into an epistemic state, most belief revision frameworks, including the AGM, incorporate solely this new information. A more natural proposal is that the agent seeks some explanation or justification first and attempts to incorporate the new information together with its justification into the agent’s current epistemic...

This is an experimental article which shows that logical correctness of logic circuits can be easily proven by the Mizar system. First, we define the notion of logic gates. Then we prove that an MSB carry of ’4 Bit Carry Skip Adder’ is equivalent to an MSB carry of a normal 4 bit adder. In the last theorem, we show that outputs of the ’4 Bit Carry Look Ahead Adder’ are equivalent to the corresp...

Feature structures are a representational device used in several current linguistic theories. This paper shows how these structures can be axiomatized in a decidable class of first-order logic, which can also be used to express constraints on these structures. Desirable properties, such as compactness and decidability, follow directly. Moreover, additional types of feature values, such as "set-...

We study various aspects of parafermionic theories such as the precise field content, a description of a basis of states (that is, the counting of independent states in a freely generated highest-weight module) and the explicit expression of the parafermionic singular vectors in completely irreducible modules. This analysis culminates in the presentation of new character formulae for the Z N pa...

Description Logics [1] are logical formalisms for representing information about classes and objects. They are very often used as the basis of knowledge representation systems and have been used recently to develop OWL semantic web language, which can be viewed as an expressive Description Logic. There is an impressive variety of Description Logics with diverse expressiveness and complexity, or...

The main task of ontology based Semantic Web is finding the accurate semantics hiding beneath the superficial representation of ontological entities. This, however, is not an easy task due to the ambiguous nature of semantics. There is a lack of systematic engineering method to guide how we comprehend semantics. Even though precise logic formulae can be used as the canonical representation of o...

Neurofibrillary pathology in Alzheimer's dementia (AD) is associated with cognitive impairments and cortical thinning, and begins in medial perirhinal cortex (mPRC) before entering entorhinal cortex (ERC). Thus, mPRC dysfunction (e.g., semantic object memory impairments) may predate or accompany ERC (i.e., episodic memory) dysfunction in the preclinical course of typical AD. We developed formul...

Neural correlates exist for a basic component of logical formulae, PREDICATE(x). Vision and audition research in primates and humans shows two independent neural pathways; one locates objects in body-centered space, the other attributes properties, such as colour, to objects. In vision these are the dorsal and ventral pathways. In audition, similarly separable "where" and "what" pathways exist....

Given a Boolean propositional formula, φ(Xn) over the basis Ω = {∧,∨,¬} we consider the following decision problem: is there a subset of literals, S, for which φ(Xn) ≡ ∧ y∈S y or φ(Xn) ≡ ∨ y∈S y? We prove that the “obvious” Σ p 2 upper bound is sub-optimal and that the problem is decidable in PNP || the class of languages decidable by polynomial time methods allowed to make non-adaptive queries...