Related papers: Statistical relational learning and neuro-symbolic…
The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation.…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
We present an implementation of a probabilistic first-order logic called TensorLog, in which classes of logical queries are compiled into differentiable functions in a neural-network infrastructure such as Tensorflow or Theano. This leads…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…
Neurosymbolic AI is a growing field of research aiming to combine neural networks learning capabilities with the reasoning abilities of symbolic systems. This hybridization can take many shapes. In this paper, we propose a new formalism for…
Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…
Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
Broadly intelligent agents should form task-specific abstractions that selectively expose the essential elements of a task, while abstracting away the complexity of the raw sensorimotor space. In this work, we present Neuro-Symbolic…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
Classical planning representation languages based on first-order logic have preliminarily been used to model and solve robotic task planning problems. Wider adoption of these representation languages, however, is hindered by the limitations…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
A recommendation system assists users in finding items that are relevant to them. Existing recommendation models are primarily based on predicting relationships between users and items and use complex matching models or incorporate…
Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…