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The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
Manipulation is a problem of fundamental importance in the context of voting in which the voters exercise their votes strategically instead of voting honestly to prevent selection of an alternative that is less preferred. The…
A general explicit upper bound is obtained for the proportion $P(n,m)$ of elements of order dividing $m$, where $n-1 \le m \le cn$ for some constant $c$, in the finite symmetric group $S_n$. This is used to find lower bounds for the…
Ensemble models are widely recognized in the ML community for their limited interpretability. For instance, while a single decision tree is considered interpretable, ensembles of trees (e.g., boosted trees) are often treated as black-boxes.…
We study the algorithmic decidability of the domination number in the Erdos-Renyi random graph model $G(n,p)$. We show that for a carefully chosen edge probability $p=p(n)$, the domination problem exhibits a strong irreducible property.…
We study the computational complexity of several scenarios of strategic behavior for the Kemeny procedure in the setting of judgment aggregation. In particular, we investigate (1) manipulation, where an individual aims to achieve a better…
When scheduling public works or events in a shared facility one needs to accommodate preferences of a population. We formalize this problem by introducing the notion of a collective schedule. We show how to extend fundamental tools from…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…
Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
Tournaments are widely used models to represent pairwise dominance between candidates, alternatives, or teams. We study the problem of providing certified explanations for why a candidate appears among the winners under various tournament…
The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups.…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
The Borda voting rule is a positional scoring rule for $z$ candidates such that in each vote, the first candidate receives $z-1$ points, the second $z-2$ points and so on. The winner in the Borda rule is the candidate with highest total…
When voter preferences are known in an incomplete (partial) manner, winner determination is commonly treated as the identification of the necessary and possible winners; these are the candidates who win in all completions or at least one…
The Gibbard-Satterthwaite theorem established that no non-trivial voting rule is strategy-proof, but that does not mean that all voting rules are equally susceptible to strategic manipulation. Over the past fifty years numerous approaches…
The study of arguments as abstract entities and their interaction as introduced by Dung (Artificial Intelligence 177, 1995) has become one of the most active research branches within Artificial Intelligence and Reasoning. A main issue for…