Related papers: Monoidal functional dependencies

We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence…

We provide a categorical framework for mathematical objects for which there is both a sort of "independent" and "dependent" composition. Namely we model them as duoidal categories in which both monoidal structures share a unit and the first…

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…

Recently, Baltag and van Benthem arXiv:2103.14946 [cs.LO] introduced a new decidable logic of functional dependence (LFD) with local dependence formulas and dependence quantifiers. The language is interpreted over dependence models, which…

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…

In this paper, we study logics of dependence on the propositional level. We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well…

This paper presents a logic of preference and functional dependence (LPFD) and its hybrid extension (HLPFD), both of whose sound and strongly complete axiomatization are provided. The decidability of LPFD is also proved. The application of…

This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or fuzzy, attributes…

Functional dependencies -- traditional, approximate and conditional are of critical importance in relational databases, as they inform us about the relationships between attributes. They are useful in schema normalization, data…

Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…

Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and modifying…

We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…

Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…

Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…

This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated…

Integrity constraints (ICs) provide a valuable tool for expressing and enforcing application semantics. However, formulating constraints manually requires domain expertise, is prone to human errors, and may be excessively time consuming,…

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Vaananen, and their compositional semantics due to Hodges. We show how Hodges' semantics can be seen as a special case of a general…

We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…

Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we…