Semiring Provenance for Guarded Logics

Dannert, Katrin M.; Grädel, Erich

doi:10.1007/978-3-030-64187-0_3

Cited by 10 publications

(10 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a way, our work can be viewed as generalizing the boolean setting considered by Barceló et al to the numerical setting. Indeed, the language MPLang can be viewed as giving a numerical semantics to positive modal logic without conjunction, following the established methodology of semiring provenance semantics for query languages [14,9], and extending the logic with application of arbitrary activation functions. By focusing on boolean inputs and outputs, Barceló et al are able to capture a stronger logic than our positive modal logic, notably, by expressing negation and counting.…”

Section: Related Workmentioning

confidence: 99%

On the expressive power of message-passing neural networks as global feature map transformers

Geerts,

Steegmans,

Bussche

2022

Preprint

View full text Add to dashboard Cite

We investigate the power of message-passing neural networks (MPNNs) in their capacity to transform the numerical features stored in the nodes of their input graphs. Our focus is on global expressive power, uniformly over all input graphs, or over graphs of bounded degree with features from a bounded domain. Accordingly, we introduce the notion of a global feature map transformer (GFMT). As a yardstick for expressiveness, we use a basic language for GFMTs, which we call MPLang. Every MPNN can be expressed in MPLang, and our results clarify to which extent the converse inclusion holds. We consider exact versus approximate expressiveness; the use of arbitrary activation functions; and the case where only the ReLU activation function is allowed.

show abstract

Section: Related Workmentioning

confidence: 99%

On the expressive power of message-passing neural networks as global feature map transformers

Geerts,

Steegmans,

Bussche

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, Dannert et al (2021) restrict the semiring even further by considering fully-chain complete semirings in order to extend provenance definition to logical languages featuring negation and fixed-point. Even if numerous useful semirings are ω-continuous, or can be extended to a such semiring, infinite provenance expressions may be considered unintuitive in some cases.…”

Section: Introductionmentioning

confidence: 99%

Revisiting Semiring Provenance for Datalog

Bourgaux¹,

Bourhis²,

Peterfreund³

et al. 2022

Preprint

View full text Add to dashboard Cite

Data provenance consists in bookkeeping meta information during query evaluation, in order to enrich query results with their trust level, likelihood, evaluation cost, and more. The framework of semiring provenance abstracts from the specific kind of meta information that annotates the data. While the definition of semiring provenance is uncontroversial for unions of conjunctive queries, the picture is less clear for Datalog. Indeed, the original definition might include infinite computations, and is not consistent with other proposals for Datalog semantics over annotated data. In this work, we propose and investigate several provenance semantics, based on different approaches for defining classical Datalog semantics. We study the relationship between these semantics, and introduce properties that allow us to analyze and compare them. Example 2. Let Σ contain r 1 := R(x, y) → H(x, x), r 2 := R(x, y) → H(x, y) and r 3 := S(x, y, z) ∧ S(x, z, y) → H(x, x). If D = {R(a, a), S(a, b, c), S(a, c, b)}, then the fact α := H(a, a) has the following derivation trees (α, r 1 , h) R(a, a) (α, r 2 , h) R(a, a) (α, r 3 , h 3 ) S(a, b, c)S(a, c, b) (α, r 3 , h ′ 3 ) S(a, c, b)S(a, b, c)whereNote that when the program at hand is recursive (i.e., the dependency graph of its atoms contain cycles) a fact may our results are valid under this assumption as well.

show abstract

“…The overall value of the formula is then a polynomial that describes precisely what combinations of literals prove the truth of the formula. Semiring semantics has been studied for various logics [1,7,8,9,15], following the successful development of semiring provenance in database theory and related fields (see e.g. [10,12,18,19,23,24,25]).…”

Section: Introductionmentioning

confidence: 99%

Semiring Provenance for Büchi Games: Strategy Analysis with Absorptive Polynomials

Grädel

Lücking

Naaf

2021

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

This paper presents a case study for the application of semiring semantics for fixed-point formulae to the analysis of strategies in Büchi games. Semiring semantics generalizes the classical Boolean semantics by permitting multiple truth values from certain semirings. Evaluating the fixed-point formula that defines the winning region in a given game in an appropriate semiring of polynomials provides not only the Boolean information on who wins, but also tells us how they win and which strategies they might use. This is well-understood for reachability games, where the winning region is definable as a least fixed point. The case of Büchi games is of special interest, not only due to their practical importance, but also because it is the simplest case where the fixed-point definition involves a genuine alternation of a greatest and a least fixed point.We show that, in a precise sense, semiring semantics provide information about all absorptiondominant strategies -strategies that win with minimal effort, and we discuss how these relate to positional and the more general persistent strategies. This information enables applications such as game synthesis or determining minimal modifications to the game needed to change its outcome.Due to space reasons, several proofs have been omitted and can be found in the full version [14].

show abstract

Semiring Provenance for Guarded Logics

Cited by 10 publications

References 9 publications

On the expressive power of message-passing neural networks as global feature map transformers

On the expressive power of message-passing neural networks as global feature map transformers

Revisiting Semiring Provenance for Datalog

Semiring Provenance for Büchi Games: Strategy Analysis with Absorptive Polynomials

Contact Info

Product

Resources

About