Related papers: Hunting for Tractable Languages for Judgment Aggre…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
Clustering a lexicon of words is a well-studied problem in natural language processing (NLP). Word clusters are used to deal with sparse data in statistical language processing, as well as features for solving various NLP tasks (text…
Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be…
Recently, Strength-based Argumentation Frameworks (StrAFs) have been proposed to model situations where some quantitative strength is associated with arguments. In this setting, the notion of accrual corresponds to sets of arguments that…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…
We consider a specific scenario of text aggregation, in the realm of musical harmonization. Musical harmonization shares similarities with text aggregation, however the language of harmony is more structured than general text. Concretely,…
Compositional generalization is the ability of a model to generalize to complex, previously unseen types of combinations of entities from just having seen the primitives. This type of generalization is particularly relevant to the semantic…
Autonomous systems that operate in a shared environment with people need to be able to follow the rules of the society they occupy. While laws are unique for one society, different people and institutions may use different rules to guide…
The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and…
End-to-end neural networks have achieved promising performances in natural language generation (NLG). However, they are treated as black boxes and lack interpretability. To address this problem, we propose a novel framework, heterogeneous…
In this paper, we consider the well-known modal logics $\mathbf{K}$, $\mathbf{T}$, $\mathbf{K4}$, and $\mathbf{S4}$, and we study some of their sub-propositional fragments, namely the classical Horn fragment, the Krom fragment, the…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
The management of uncertainty in expert systems has usually been left to ad hoc representations and rules of combinations lacking either a sound theory or clear semantics. The objective of this paper is to establish a theoretical basis for…
The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…
The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and…
Aggregating signals from a collection of noisy sources is a fundamental problem in many domains including crowd-sourcing, multi-agent planning, sensor networks, signal processing, voting, ensemble learning, and federated learning. The core…