An Algebra of Modular Systems: Static and Dynamic Perspectives

Ternovska, Eugenia

doi:10.1007/978-3-030-29007-8_6

Cited by 6 publications

(13 citation statements)

References 15 publications

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“…Finally, an operation that often occurs in dynamic systems is the fixed point construct used by Ternovska (2019). It remains to be seen how our work, and the further research directions mentioned above, can be extended to include the fixpoint operation.…”

Section: Discussionmentioning

confidence: 98%

“…The converse of a BRV A is defined to be {(ν 2 , ν 1 ) | (ν 1 , ν 2 ) ∈ A}. In the context of LIF (Ternovska 2019) it can model constraint solving by searching for an input to a module that produces a desired outcome. When we add converse to LIF with only a single variable (|V| = 1), and the vocabulary has only binary relations of input arity one, then we obtain the classical calculus of relations (Tarski 1941).…”

Section: Discussionmentioning

confidence: 99%

“…The Logic of Information Flows (LIF) (Ternovska 2017;Ternovska 2019) is a knowledge representation framework designed to model and understand how information propagates in complex systems, and to find ways to navigate it efficiently. The basic idea is that modules, that can be given procedurally or declaratively, are the atoms of a logic whose syntax resembles first-order logic, but whose semantics produces new modules.…”

Section: Introductionmentioning

confidence: 99%

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

Aamer

Bogaerts

Surinx

et al. 2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

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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.

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Section: Discussionmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Aamer

Bogaerts

Surinx

et al. 2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

Self Cite

View full text Add to dashboard Cite

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“…Moreover, it was not clear to us how to even approach the problem of modular system containment in that formalism. The algebra of (Ternovska 2019) is similar to ours, but it also does not differentiate between abstract and concrete modules. The main focus of that work is on a transition from a static algebra to a dynamic one, and to a related modal dynamic logic.…”

Section: Introductionmentioning

confidence: 91%

Algebra of Modular Systems: Containment and Equivalence

Bulatov

Ternovska

2021

AAAI

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The Algebra of Modular System is a KR formalism that allows for combinations of modules written in multiple languages. Informally, a module represents a piece of knowledge. It can be given by a knowledge base, be an agent, an ASP, ILP, CP program, etc. Formally, a module is a class of structures over the same vocabulary. Modules are combined declaratively, using, essentially, operations of Codd's relational algebra. In this paper, we address the problem of checking modular system containment, which we relate to a homomorphism problem. We prove that, for a large class of modular systems, the containment problem (and thus equivalence) is in the complexity class NP, and therefore is solvable by, e.g., SAT solvers. We discuss conditions under which the problem is polynomial time solvable.

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“…As discussed in the next section, there are also various proposals for defining a semantics for the communication of arbitrarily heterogenous computational modules [80]. It would be interesting to see whether SP could be further extended along those lines.…”

Section: Compositionmentioning

confidence: 99%

Semiring programming: A semantic framework for generalized sum product problems

Belle

Raedt

2020

International Journal of Approximate Reasoning

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To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration amongst these, contemporary representation methodologies offer little support for this.In an attempt to alleviate this situation, we position and motivate a new declarative programming framework in this paper. We focus on the semantical foundations in service of providing abstractions of well-known problems such as SAT, Bayesian inference, generative models, learning and convex optimization. Programs are understood in terms of first-order logic structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines and represent non-standard problems over unbounded domains. Thus, the main thrust of this paper is to view such well-known problems through a unified lens in the hope that appropriate solver strategies (exact, approximate, portfolio or hybrid) may emerge that tackle real-world problems in a principled way.

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An Algebra of Modular Systems: Static and Dynamic Perspectives

Cited by 6 publications

References 15 publications

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

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

Algebra of Modular Systems: Containment and Equivalence

Semiring programming: A semantic framework for generalized sum product problems

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