Related papers: Generalized Absorptive Polynomials and Provenance …
Semiring parsing is an elegant framework for describing parsers by using semiring weighted logic programs. In this paper we present a generalization of this concept: latent-variable semiring parsing. With our framework, any semiring…
In today's data-driven ecosystems, ensuring data integrity, traceability and accountability is important. Provenance polynomials constitute a powerful formalism for tracing the origin and the derivations made to produce database query…
We study the first-order axiomatisability of finite semiring interpretations or, equivalently, the question whether elementary equivalence and isomorphism coincide for valuations of atomic facts over a finite universe into a commutative…
We study various notions of dependency in semiring team semantics. Semiring teams are essentially database relations, where each tuple is annotated with some element from a positive semiring. We consider semiring generalizations of several…
Ontology-based data access (OBDA) is a popular paradigm for querying heterogeneous data sources by connecting them through mappings to an ontology. In OBDA, it is often difficult to reconstruct why a tuple occurs in the answer of a query.…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
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…
Binary semirings such as the tropical, log, and probability semirings form a core algebraic tool in classical and modern neural inference systems, supporting tasks like Viterbi decoding, dynamic programming, and probabilistic reasoning.…
In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…
The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The…
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…
The rule $\mathrm{Defeated}(x) \leftarrow \mathrm{Attacks}(y,x),\, \neg \, \mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF).…
Advanced Persistent Threats (APTs) have caused significant losses across a wide range of sectors, including the theft of sensitive data and harm to system integrity. As attack techniques grow increasingly sophisticated and stealthy, the…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
We study in this paper provenance information for queries with aggregation. Provenance information was studied in the context of various query languages that do not allow for aggregation, and recent work has suggested to capture provenance…