Related papers: Cooperation between Top-Down and Bottom-Up Theorem…
Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate…
We initiate an investigation of learning tasks in a setting where the learner is given access to two competing provers, only one of which is honest. Specifically, we consider the power of such learners in assessing purported properties of…
"Forward-only" algorithms, which train neural networks while avoiding a backward pass, have recently gained attention as a way of solving the biologically unrealistic aspects of backpropagation. Here, we first address compelling challenges…
In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the…
This paper describes how XSB combines top-down and bottom-up computation through the mechanisms of variant tabling and subsumptive tabling with abstraction, respectively. It is well known that top-down evaluation of logical rules in Prolog…
Probes trained on model activations can detect undesirable behaviors like deception or biases that are difficult to identify from outputs alone. This makes them useful detectors to identify misbehavior. Furthermore, they are also valuable…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Modern statistical analyses often involve testing large numbers of hypotheses. In many situations, these hypotheses may have an underlying tree structure that not only helps determine the order that tests should be conducted but also…
Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
One of the challenges of open-ended learning in robots is the need to autonomously discover goals and learn skills to achieve them. However, when in lifelong learning settings, it is always desirable to generate sub-goals with their…
Despite the somewhat different techniques used in developing search engines and recommender systems, they both follow the same goal: helping people to get the information they need at the right time. Due to this common goal, search and…
Deep learning models loosely mimic bottom-up signal pathways from low-order sensory areas to high-order cognitive areas. After training, DL models can outperform humans on some domain-specific tasks, but their decision-making process has…
Large language model (LLM) agents on multi-step tasks suffer reasoning degradation, looping, drift, stuck states, at rates up to 30% on hard tasks. Current solutions include hard step limits (abrupt) or LLM-as-judge monitoring (10-15%…
E prover is a state-of-the-art theorem prover for first-order logic with equality. E prover is built around a saturation loop, where new clauses are derived by inference rules from previously derived clauses. Selection of clauses for the…
A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…
Training conversational question-answering (QA) systems requires a substantial amount of in-domain data, which is often scarce in practice. A common solution to this challenge is to generate synthetic data. Traditional methods typically…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
Efficiently tackling combinatorial reasoning problems, particularly the notorious NP-hard tasks, remains a significant challenge for AI research. Recent efforts have sought to enhance planning by incorporating hierarchical high-level search…
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…