Related papers: On Learning to Prove
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
This paper experimentally studies whether individuals hold a first-order belief that others apply Bayes' rule to incorporate private information into their beliefs, which is a fundamental assumption in many Bayesian and non-Bayesian social…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…
We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
Probably the most important problem in machine learning is the preliminary biasing of a learner's hypothesis space so that it is small enough to ensure good generalisation from reasonable training sets, yet large enough that it contains a…
Existing learning from demonstration algorithms usually assume access to expert demonstrations. However, this assumption is limiting in many real-world applications since the collected demonstrations may be suboptimal or even consist of…
We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our…
This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning…
In this paper we investigate the potential for persuasion arising from the quantum indeterminacy of a decision-maker's beliefs, a feature that has been proposed as a formal expression of well-known cognitive limitations. We focus on a…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…