Related papers: Generalizing Redundancy in Propositional Logic: Fo…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…
Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
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…
Feature weighting algorithms try to solve a problem of great importance nowadays in machine learning: The search of a relevance measure for the features of a given domain. This relevance is primarily used for feature selection as feature…
Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of…
We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear k-CNF formulas with at most 4k^2 4^k clauses, and on the other hand, any linear k-CNF formula with at most…
For argumentation mining, there are several sub-tasks such as argumentation component type classification, relation classification. Existing research tends to solve such sub-tasks separately, but ignore the close relation between them. In…
We present a logical system CFP (Concurrent Fixed Point Logic) from whose proofs one can extract nondeterministic and concurrent programs that are provably total and correct with respect to the proven formula. CFP is an intuitionistic…
The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal…
The unification problem in a propositional logic is to determine, given a formula F, whether there exists a substitution s such that s(F) is in that logic. In that case, s is a unifier of F. When a unifiable formula has minimal complete…
Recurrent neural networks are convenient and efficient models for language modeling. However, when applied on the level of characters instead of words, they suffer from several problems. In order to successfully model long-term…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…
For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…
This paper aims to define, quantify, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method disentangles feature…
We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria,…
A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework encompasses problems previously proposed by Huffman, Campbell, Nath, and Drmota and…
Natural language (NL) documentation is the bridge between software managers and testers, and NL test cases are prevalent in system-level testing and other quality assurance activities. Due to reasons such as requirements redundancy,…