Sequential decomposition of propositional logic programs

• URL: http://arxiv.org/abs/2304.13522v2
• Date: Thu, 14 Sep 2023 15:25:00 GMT
• Title: Sequential decomposition of propositional logic programs
• Authors: Christian Anti\'c
• Abstract summary: This paper studies the sequential decomposition of programs by studying Green's relations between programs. In a broader sense, this paper is a further step towards an algebraic theory of logic programming.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory -- between programs. In a broader sense, this paper is a further step towards an algebraic theory of logic programming.

Related papers

• Argumentative Characterizations of (Extended) Disjunctive Logic Programs [2.055949720959582]
  We show that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs and their extensions. We consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect.
  arXiv  Detail & Related papers  (2023-06-12T14:01:38Z)
• The Transformation Logics [58.35574640378678]
  We introduce a new family of temporal logics designed to balance the trade-off between expressivity and complexity. Key feature is the possibility of defining operators of a new kind that we call transformation operators. We show them to yield logics capable of creating hierarchies of increasing expressivity and complexity.
  arXiv  Detail & Related papers  (2023-04-19T13:24:04Z)
• Discourse-Aware Graph Networks for Textual Logical Reasoning [142.0097357999134]
  Passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence) We propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs) The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features.
  arXiv  Detail & Related papers  (2022-07-04T14:38:49Z)
• A Formalisation of Abstract Argumentation in Higher-Order Logic [77.34726150561087]
  We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using interactive and automated reasoning tools.
  arXiv  Detail & Related papers  (2021-10-18T10:45:59Z)
• On syntactically similar logic programs and sequential decompositions [0.0]
  Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer science and science in general. We show how similarity can be used to answer queries across different domains via a one-step reduction.
  arXiv  Detail & Related papers  (2021-09-11T15:22:17Z)
• Sequential composition of answer set programs [0.0]
  This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. In a broader sense, this paper is a first step towards an algebra of answer set programs and in the future we plan to lift the methods of this paper to wider classes of programs.
  arXiv  Detail & Related papers  (2021-04-25T13:27:22Z)
• Representing Partial Programs with Blended Abstract Semantics [62.20775388513027]
  We introduce a technique for representing partially written programs in a program synthesis engine. We learn an approximate execution model implemented as a modular neural network. We show that these hybrid neuro-symbolic representations enable execution-guided synthesizers to use more powerful language constructs.
  arXiv  Detail & Related papers  (2020-12-23T20:40:18Z)
• Latent Programmer: Discrete Latent Codes for Program Synthesis [56.37993487589351]
  In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically meant for search: rich enough to specify the desired output but compact enough to make search more efficient. We introduce the emphLatent Programmer, a program synthesis method that first predicts a discrete latent code from input/output examples, and then generates the program in the target language.
  arXiv  Detail & Related papers  (2020-12-01T10:11:35Z)
• RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs [91.71504177786792]
  This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks. Existing methods either suffer from the problem of searching in a large search space or ineffective optimization due to sparse rewards.
  arXiv  Detail & Related papers  (2020-10-08T14:47:02Z)
• Sequential composition of propositional logic programs [0.0]
  We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for arbitrary programs. We show that the immediate consequence operator of a program can be represented via composition which allows us to compute its least model without any explicit reference to operators.
  arXiv  Detail & Related papers  (2020-09-12T11:57:30Z)
• Verifying Tight Logic Programs with anthem and Vampire [7.804960968120875]
  We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo. We study the relationship between stable models and completion in this context, and describe preliminary experiments with the use of two software tools.
  arXiv  Detail & Related papers  (2020-08-05T10:01:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.