Related papers: On Concise Encodings of Preferred Extensions
The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and…
This paper maps out the relation between different approaches for handling preferences in argumentation with strict rules and defeasible assumptions by offering translations between them. The systems we compare are: non-prioritized defeats…
In this paper, we address an issue of finding explainable clusters of class-uniform data in labelled datasets. The issue falls into the domain of interpretable supervised clustering. Unlike traditional clustering, supervised clustering aims…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference…
We discover a connection between finding subset-maximal repairs for sets of functional and inclusion dependencies, and computing extensions within argumentation frameworks (AFs). We study the complexity of the existence of a repair and…
We present a declarative language, PP, for the high-level specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express non-trivial, multi-dimensional…
Subshifts are sets of colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissible completions. Since soficity of $\mathbb{Z}$ subshifts is…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Argumentation accommodates various rhetorical devices, such as questions, reported speech, and imperatives. These rhetorical tools usually assert argumentatively relevant propositions rather implicitly, so understanding their true meaning…
We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO$^2$ and the guarded fragment GF. We prove that…
Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision…
Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and…
The domain of explainable AI is of interest in all Machine Learning fields, and it is all the more important in clustering, an unsupervised task whose result must be validated by a domain expert. We aim at finding a clustering that has high…
Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling,…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
A preferential arrangement of a finite set is an ordered partition. Associated with each such ordered partition is a chain of subsets or blocks endowed with a linear order. The chain may be split into sections by the introduction of a…