Related papers: Negotiation sets: a general framework
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and…
In the present note we study certain arrangements of codimension $2$ flats in projective spaces, we call them "Fermat arrangements". We describe algebraic properties of their defining ideals. In particular, we show that they provide…
The following three types of objects are considered in a dual functorial formalism: (i) ind-scheme of mappings between two schemes, (ii) for a quantum group G, ind-scheme of G-mappings between two G-schemes, and (iii) ind-scheme of group…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
Closure operations such as tight and integral closure and test ideals have appeared frequently in the study of commutative algebra. This articles serves as a survey of the authors' prior results connecting closure operations, test ideals,…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…
This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…
Meaning negotiation (MN) is the general process with which agents reach an agreement about the meaning of a set of terms. Artificial Intelligence scholars have dealt with the problem of MN by means of argumentations schemes, beliefs merging…
I argue that, on a judicious reading of two existing criteria--one syntactic and the other semantic--dual theories can be taken to be empirically equivalent. The judicious reading is straightforward, but leads to the surprising conclusion…
In this work, we first define intuitionistic fuzzy parametrized soft sets (intuitionistic FP-soft sets) and study some of their properties. We then introduce an adjustable approaches to intuitionistic FP-soft sets based decision making. We…
This paper argues that certain ontology design problems are profitably addressed by treating ontologies as theories and by defining a set of operations that create new ontologies, including their constraints, out of other ontologies. The…
Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…
Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…
We revisit the duality between Kripke and algebraic semantics of intuitionistic and intuitionistic modal logic. We find that there is a certain mismatch between the two semantics, which means that not all algebraic models can be embedded…