Related papers: Learning Formal Mathematics From Intrinsic Motivat…
Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
Reward design is a critical part of the application of reinforcement learning, the performance of which strongly depends on how well the reward signal frames the goal of the designer and how well the signal assesses progress in reaching…
The ability to precisely derive mathematical objects is a core requirement for downstream STEM applications, including mathematics, physics, and chemistry, where reasoning must culminate in formally structured expressions. Yet, current LM…
How do cognitive agents decide what is the relevant information to learn and how goals are selected to gain this knowledge? Cognitive agents need to be motivated to perform any action. We discuss that emotions arise when differences between…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
We show a data-driven approach to discover the underlying structural form of the mathematical equation governing the dynamics of multiple but similar systems induced by the same mechanisms. This approach hinges on theories that we lay out…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Humans and animals explore their environment and acquire useful skills even in the absence of clear goals, exhibiting intrinsic motivation. The study of intrinsic motivation in artificial agents is concerned with the following question:…
We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
As large language models (LLMs) advance their mathematical capabilities toward the IMO level, the scarcity of challenging, high-quality problems for training and evaluation has become a significant bottleneck. Simultaneously, recent code…
We will focus on the Quantum theory and starting from simple philosophical conjectures, we infer possible different physical realities. Also we argue of possible wavefunction emerging under specific conditions of the physical reality.…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…
We present a novel intrinsically motivated agent that learns how to control the environment in the fastest possible manner by optimizing learning progress. It learns what can be controlled, how to allocate time and attention, and the…
Engineering needs mathematics, but the converse is also increasingly evident. Indeed, mathematics is still recovering from the drawbacks of several "reforms". Encouraging is the revived interest in proofs indicated by various recent…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…