Inputs, Outputs, and Composition in the Logic of Information Flows

Abstract

The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this paper is to propose semantic and syntactic definitions of inputs and outputs of LIF expressions. We study how the two relate and show that our syntactic definition is optimal in a sense that is made precise. The second contribution of this paper is a systematic study of the expressive power of sequential composition in LIF. Our results on composition tie in the results on inputs and outputs, and relate LIF to first-order logic (FO) and bounded-variable LIF to bounded-variable FO.

Algebra of Modular Systems: Containment and Equivalence

“…An important future extension of our work would be to the Unions of Conjunctive Compound Modules, using Sagiv-Yannakakis theorem (Sagiv and Yannakakis 1980). We would also like to prove a Containment property for an efficient restriction of a dynamic version of the algebra (Ternovska 2019), where inputs and outputs of modules are specified, similarly to (Aamer et al 2020a) and (Aamer et al 2020b).…”

An Algebra of Combined Constraint Solving

“…The syntax allows only one such (free) variable per an algebraic expression. 3 of all relational τ -structures over the same finite domain. We require that P, Q ∈ τ reg .…”

“…It outputs only the longest, in terms of the number of f -steps, transition out of all possible transitions from the same state produced by the Kleene star. 4 Binary op 2 : F 2 → F (partial mappings on strings in U + that depend on two functions): op 2 ∈ {;, ⊔} These operations take two functions as arguments, and combine them to obtain a (partial) mapping on U + . Sequential Composition (f ;g)(x) is the standard function composition g(f (x)).…”

“…Recall that terms are interpreted as partial functions, see (3). This is crucial for reasoning about computations (cf.…”

“…A version of LIF, [50], was published, initially, in the context of reasoning about modular systems, and was based on classical logic. In subsequent work, with a group of coauthors, we studied the notions of input, output and composition [4], [2] in LIF, and applications to data access in database research [3]. A short description of that work can be found in [51].…”