Related papers: Generalization of Clauses under Implication

Reinforcement learning is an essential paradigm for solving sequential decision problems under uncertainty. Despite many remarkable achievements in recent decades, applying reinforcement learning methods in the real world remains…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…

The notion of generalization has moved away from the classical one defined in statistical learning theory towards an emphasis on out-of-domain generalization (OODG). There has been a growing focus on generalization from easy to hard, where…

In-context learning (ICL) is an important paradigm for adapting large language models (LLMs) to new tasks, but the generalization behavior of ICL remains poorly understood. We investigate the inductive biases of ICL from the perspective of…

It is evidence that representation learning can improve model's performance over multiple downstream tasks in many real-world scenarios, such as image classification and recommender systems. Existing learning approaches rely on establishing…

The Tsetlin Machine (TM) architecture has recently demonstrated effectiveness in Machine Learning (ML), particularly within Natural Language Processing (NLP). It has been utilized to construct word embedding using conjunctive propositional…

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…

In this article, we introduce a novel variant of the Tsetlin machine (TM) that randomly drops clauses, the key learning elements of a TM. In effect, TM with drop clause ignores a random selection of the clauses in each epoch, selected…

Modern learning systems increasingly rely on amortized learning - the idea of reusing computation or inductive biases shared across tasks to enable rapid generalization to novel problems. This principle spans a range of approaches,…

An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…

As real logic programmers normally use cut (!), an effective learning procedure for logic programs should be able to deal with it. Because the cut predicate has only a procedural meaning, clauses containing cut cannot be learned using an…

Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…

Reasoning is an important task for large language models (LLMs). Among all the reasoning paradigms, inductive reasoning is one of the fundamental types, which is characterized by its particular-to-general thinking process and the…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short…

Standard approaches in generalizability often focus on generalizing the intent-to-treat (ITT). However, in practice, a more policy-relevant quantity is the generalized impact of an intervention across compliers. While instrumental variable…

A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…

Interpreting the internal process of neural models has long been a challenge. This challenge remains relevant in the era of large language models (LLMs) and in-context learning (ICL); for example, ICL poses a new issue of interpreting which…