Related papers: Learning Formal Mathematics From Intrinsic Motivat…

When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…

Exploring rich environments and evaluating one's actions without prior knowledge is immensely challenging. In this paper, we propose Motif, a general method to interface such prior knowledge from a Large Language Model (LLM) with an agent.…

Existing approaches to learning to prove theorems focus on particular logics and datasets. In this work, we propose Monte-Carlo simulations guided by reinforcement learning that can work in an arbitrarily specified logic, without any human…

Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…

We define a class of formal systems inspired by Prawitz's theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to…

The study of exploration in the domain of decision making has a long history but remains actively debated. From the vast literature that addressed this topic for decades under various points of view (e.g., developmental psychology,…

Epistemology is the branch of philosophy that deals with gaining knowledge. It is closely related to ontology. The branch that deals with questions like "What is real?" and "What do we know?" as it provides these components. When using…

One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…

We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a…

As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having…

Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…

A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to…

Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…

Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…

Reinforcement Learning faces an important challenge in partial observable environments that has long-term dependencies. In order to learn in an ambiguous environment, an agent has to keep previous perceptions in a memory. Earlier memory…

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…

People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic…

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to…