Related papers: Logical reduction of relations: from relational da…
This paper presents a thoroughgoing interpretation of a weak relevant logic built over the Dunn-Belnap four-valued semantics in terms of the communication of information in a network of sites of knowledge production (laboratories). The…
Natural language understanding's relation extraction makes innovative and encouraging novel business concepts possible and facilitates new digitilized decision-making processes. Current approaches allow the extraction of relations with a…
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with…
We discuss an algebraic approach to propositional logic with side effects. To this end, we use Hoare's conditional [1985], which is a ternary connective comparable to if-then-else. Starting from McCarthy's notion of sequential evaluation…
Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…
The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to…
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use…
We introduce a relational approach to program synthesis. The key idea is to decompose synthesis tasks into simpler relational synthesis subtasks. Specifically, our representation decomposes a training input-output example into sets of input…
In this report we tell the story of the notion "reduction of couplings" as we witnessed it in the course of time. Born as an innocent child of renormalization theory it first served the study of asymptotic behavior of several couplings in a…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a…
We show a new reduction method on a simplicial complex. This reduction works well with relations and Dowker complexes. The idea is to add a dummy vertex $ z $ to the simplicial complex $K$. We add the simplicial cone $ z * L $ to $K$ where…
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 justify generalisations of weak values from a tentatively relational perspective by deriving them from a generalisation of Bayes' rule. We also argue that these generalisations have implications of quantum nonlocality and may form a…
This article contributes to the debate of the meaning of relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues for today's leading…
We study the Laurent property, the irreducibility and the coprimeness for lattice equations (partial difference equations), mainly focusing on how the choice of initial value problem (the choice of domain) affects these properties. We show…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…
In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…