Related papers: Redundancy in Logic I: CNF Propositional Formulae
Explanations play a variety of roles in various recommender systems, from a legally mandated afterthought, through an integral element of user experience, to a key to persuasiveness. A natural and useful form of an explanation is the…
Large Language Models (LLMs) rely on generating extensive intermediate reasoning units (e.g., tokens, sentences) to enhance final answer quality across a wide range of complex tasks. While this approach has proven effective, it inevitably…
In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It…
Bachmair's and Ganzinger's abstract redundancy concept for the Superposition Calculus justifies almost all operations that are used in superposition provers to delete or simplify clauses, and thus to keep the clause set manageable. Typical…
Recent large language models have shown promising capabilities in long-form reasoning, following structured chains of thought before arriving at a final answer. However, we observe that these reasoning paths tend to include substantial…
This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…
Some existing notions of redundancy among association rules allow for a logical-style characterization and lead to irredundant bases of absolutely minimum size. One can push the intuition of redundancy further and find an intuitive notion…
I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…
Generalizing the novel clause elimination procedures developed in [M. Heule, M. J\"arvisalo, and A. Biere. Clause elimination procedures for CNF formulas. In Proc. LPAR-17, volume 6397 of LNCS, pages 357-371. Springer, 2010.], we introduce…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
Large language models (LLMs) generate outputs by utilizing extensive context, which often includes redundant information from prompts, retrieved passages, and interaction history. In critical applications, it is vital to identify which…
The Aristotelian syllogistic cannot account for the validity of many inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a)…
This paper shows that, even at the most basic level, the parallel, countable branching and uncountable branching recurrences of Computability Logic (see http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles.
Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Recent years have witnessed an increasing interest in training machines with reasoning ability, which deeply relies on accurately and clearly presented clue forms. The clues are usually modeled as entity-aware knowledge in existing studies.…
A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
In this paper we take closer look at recent developments for the chase procedure, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central…