Direct-optimal basis computation by means of the fusion of simplification rules

Rodríguez‐Lorenzo, Estrella; Bertet, Karell; Enciso, Manuel; Mora, Ángel

doi:10.1016/j.dam.2017.12.031

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…An implication system Σ defined on a set S is a binary relation on P(S) and consists of a set of implication rules A → B, where A, B ∈ P(S). The family F that satisfies all and the simplification equivalence [167,166]:…”

Section: Knowlegde Representationmentioning

confidence: 99%

The Horn Non-Clausal Class and its Polynomiality

Imaz¹

2021

Preprint

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The expressiveness of propositional non-clausal (NC) formulas is exponentially richer than that of clausal formulas. Yet, clausal efficiency outperforms non-clausal one. Indeed, a major weakness of the latter is that, while Horn clausal formulas, along with Horn algorithms, are crucial for the high efficiency of clausal reasoning, no Horn-like formulas in non-clausal form had been proposed.To overcome such weakness, we define the hybrid class H NC of Horn Non-Clausal (Horn-NC) formulas, by adequately lifting the Horn pattern to NC form, and argue that H NC , along with future Horn-NC algorithms, shall increase non-clausal efficiency just as the Horn class has increased clausal efficiency.Secondly, we: (i) give the compact, inductive definition of H NC ; (ii) prove that syntactically H NC subsumes the Horn class but semantically both classes are equivalent, and (iii) characterize the non-clausal formulas belonging to H NC .Thirdly, we define the Non-Clausal Unit-Resolution calculus, UR NC , and prove that it checks the satisfiability of H NC in polynomial time. This fact, to our knowledge, makes H NC the first characterized polynomial class in NC reasoning.Finally, we prove that H NC is linearly recognizable, and also that it is both strictly succincter and exponentially richer than the Horn class.We discuss that in NC automated reasoning, e.g. satisfiability solving, theorem proving, logic programming, etc., can directly benefit from H NC and UR NC and that, as a by-product of its proved properties, H NC arises as a new alternative to analyze Horn functions and implication systems.

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Section: Knowlegde Representationmentioning

confidence: 99%

The Horn Non-Clausal Class and its Polynomiality

Imaz¹

2021

Preprint

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“…The inference rules of SL are enough to compute all the models and their main advantage is that they can be seen as logical equivalence rules (see Proposition 2), providing a transformation stronger than that of the usual inference rules. These equivalences have opened the door to the development of several automated methods to manage implications by using Logic, for instance: to compute the syntactic attribute closure [7], to reduce the specification of implications [6], to compute several kinds of basis of implications [8,14] and, the one that has inspired this work, to compute all minimal generators and closed sets [15].…”

Section: Definition 2 [Syntax and Semantics Of Sl]mentioning

confidence: 99%

“…In previous works [6][7][8], several logic-based algorithms have been introduced to efficiently manage implications with different purposes (redundancy removal, transformation of implicational sets, etc.). In this paper, given a dataset, we extract a knowledge-base in terms of attribute implications and the minimal generators of this knowledge-base are used to drive the recommendation process.…”

Section: Introductionmentioning

confidence: 99%

A Formal Concept Analysis Approach to Cooperative Conversational Recommendation

Enciso¹,

Mora²,

Ojeda‐Aciego³

et al. 2020

IJCIS

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We focus on the development of a method to guide the choice of a set of users in an environment where the number of features describing the items is high and user interaction becomes laborious. Using the framework of formal concept analysis, particularly the notion of implication between attributes, we propose a method strongly based on logic which allows to manage the users' preferences by following a conversational paradigm. Concerning complexity, to build the conversation and provide updated information based on the users' previous actions (choices) the method has polynomial delay.

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