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Extended multi-adjoint logic programming

M. Eugenia Cornejo, David Lobo, Jesús Medina

TL;DR

This work extends multi-adjoint logic programming by introducing EMALP, which integrates constraints and extended aggregators to support multiple negations under stable-model semantics. It develops two translation pipelines: EMALP to constraint-free EMALP and constraint-free EMALP to MANLP, with formal proofs that stable models are preserved across translations. These results enable applying established MANLP theory to EMALPs and facilitate mapping natural-language or database information into decision rules within a unified semantic framework. The contributions broaden the algebraic and semantic foundations of logic programming, offering flexible methods to encode complex reasoning tasks and analyze existence and uniqueness of stable models.

Abstract

Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to consider, for example, different negation operators in the body of the rules of a logic program. We have introduced the syntax and the semantics of this new paradigm, as well as an interesting mechanism for obtaining a multi-adjoint normal logic program from an extended multi-adjoint logic program. This mechanism will allow us to establish technical properties relating the different stable models of both logic programming frameworks. Moreover, it makes possible that the already developed and future theory associated with stable models of multi-adjoint normal logic programs can be applied to extended multi-adjoint logic programs.

Extended multi-adjoint logic programming

TL;DR

This work extends multi-adjoint logic programming by introducing EMALP, which integrates constraints and extended aggregators to support multiple negations under stable-model semantics. It develops two translation pipelines: EMALP to constraint-free EMALP and constraint-free EMALP to MANLP, with formal proofs that stable models are preserved across translations. These results enable applying established MANLP theory to EMALPs and facilitate mapping natural-language or database information into decision rules within a unified semantic framework. The contributions broaden the algebraic and semantic foundations of logic programming, offering flexible methods to encode complex reasoning tasks and analyze existence and uniqueness of stable models.

Abstract

Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to consider, for example, different negation operators in the body of the rules of a logic program. We have introduced the syntax and the semantics of this new paradigm, as well as an interesting mechanism for obtaining a multi-adjoint normal logic program from an extended multi-adjoint logic program. This mechanism will allow us to establish technical properties relating the different stable models of both logic programming frameworks. Moreover, it makes possible that the already developed and future theory associated with stable models of multi-adjoint normal logic programs can be applied to extended multi-adjoint logic programs.
Paper Structure (6 sections, 9 theorems, 100 equations)

This paper contains 6 sections, 9 theorems, 100 equations.

Table of Contents

  1. Introduction
  2. Multi-adjoint normal logic programming
  3. Extending multi-adjoint normal logic programs
  4. Translating EMALPs into constraint-free EMALPs.
  5. Translating constraint-free EMALP into MANLP
  6. Conclusions and future work

Key Result

Theorem 1

Let $(K,\preceq,\leftarrow_1,\mathop{\&}\nolimits_1,\dots,\leftarrow_n,\mathop{\&}\nolimits_n,\neg )$ be a multi-adjoint normal lattice, where $K$ is a non-empty convex compact subset of an euclidean space, and $\mathbb{P}$ be a finite MANLP defined on this lattice. If $\mathop{\&}\nolimits_1,\dots,

Theorems & Definitions (29)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • definition 5
  • definition 6
  • definition 7
  • Theorem 1: fss:manlp2017
  • definition 8
  • definition 9
  • ...and 19 more