Related papers: The Horn Non-Clausal Class and its Polynomiality
We present a compositional SMT-based algorithm for safety of procedural C programs that takes the heap into consideration as well. Existing SMT-based approaches are either largely restricted to handling linear arithmetic operations and…
Understanding causal heterogeneity is essential for scientific discovery in domains such as biology and medicine. However, existing methods lack causal awareness, with insufficient modeling of heterogeneity, confounding, and observational…
Cost and cardinality estimation is vital to query optimizer, which can guide the plan selection. However traditional empirical cost and cardinality estimation techniques cannot provide high-quality estimation, because they cannot capture…
It is well understood that different neural network architectures are suited to different tasks, but is there always a single best architecture for a given task? We compare the expressive power of transformers, RNNs, and transformers with…
Distilling from a knowledge base only the part that is relevant to a subset of alphabet, which is recognized as forgetting, has attracted extensive interests in AI community. In standard propositional logic, a general algorithm of…
Conjunctive query answering over expressive Horn Description Logic ontologies is a relevant and challenging problem which, in some cases, can be addressed by application of the chase algorithm. In this paper, we define a novel acyclicity…
We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with…
We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then…
We study the complexity and expressive power of conjunctive queries over unranked labeled trees represented using a variety of structure relations such as ``child'', ``descendant'', and ``following'' as well as unary relations for node…
We show that it is possible to craft transformations that, applied to compositional grammars, result in grammars that neural networks can learn easily, but humans do not. This could explain the disconnect between current metrics of…
Linear type theories, of various types and kinds, are of fundamental importance in most programming language research nowadays. In this paper we describe an extension of Benton's Linear-Non-Linear type theory and model for which we can…
One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…
We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…
Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…
Counting the number of answers to conjunctive queries is a fundamental problem in databases that, under standard assumptions, does not have an efficient solution. The issue is inherently #P-hard, extending even to classes of acyclic…
The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…