Related papers: Redundancy in Logic I: CNF Propositional Formulae

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…

Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be less-incomplete than other. Neutrosophy is less-incomplete than many other systems because it contains them.…

We consider the problem of predicting plausible missing facts in relational data, given a set of imperfect logical rules. In particular, our aim is to provide bounds on the (expected) number of incorrect inferences that are made in this…

Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…

Evidence plays a crucial role in automated fact-checking. When verifying real-world claims, existing fact-checking systems either assume the evidence sentences are given or use the search snippets returned by the search engine. Such methods…

Convertibility checking - determining whether two lambda-terms are equal up to reductions - is a crucial component of proof assistants and dependently-typed languages. Practical implementations often use heuristics to quickly conclude that…

How to extract negative information from programs is an important issue in logic programming. Here we address the problem for functional logic programs, from a proof-theoretic perspective. The starting point of our work is CRWL (Constructor…

We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…

We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…

Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…

RRULES is presented as an improvement and optimization over RULES, a simple inductive learning algorithm for extracting IF-THEN rules from a set of training examples. RRULES optimizes the algorithm by implementing a more effective mechanism…

The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at…

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…

Language models (LMs) may appear insensitive to word order changes in natural language understanding (NLU) tasks. In this paper, we propose that linguistic redundancy can explain this phenomenon, whereby word order and other linguistic cues…

Existential positive formulas form a fragment of first-order logic that includes and is semantically equivalent to unions of conjunctive queries, one of the most important and well-studied classes of queries in database theory. We consider…

We consider the problem of finding plausible knowledge that is missing from a given ontology, as a generalisation of the well-studied taxonomy expansion task. One line of work treats this task as a Natural Language Inference (NLI) problem,…

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every…

Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular…