Related papers: Semantics of Conjectures
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
We present the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may…
The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any…
Rough sets are approximations of concrete sets. The theory of rough sets has been used widely for data-mining. While it is well-known that adjunctions are underlying in rough approximations, such adjunctions are not enough for…
We describe an inventory of semantic relations that are expressed by prepositions. We define these relations by building on the word sense disambiguation task for prepositions and propose a mapping from preposition senses to the relation…
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this…
A software architecture is the result of multiple decisions made by a software architect. These decisions are called architectural decisions, as they bring solutions to architectural problems. Relations between decisions can be captured in…
Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
Over the past 50 years many have debated what representation should be used to capture the meaning of natural language utterances. Recently new needs of such representations have been raised in research. Here I survey some of the…
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according…
This paper develops a new approach to computational argumentation that is informed by philosophical and linguistic views. Namely, it takes into account two ideas that have received little attention in the literature on computational…
A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions…