{
  "id": "2205.01269",
  "version": "v1",
  "published": "2022-05-03T01:55:56.000Z",
  "updated": "2022-05-03T01:55:56.000Z",
  "title": "Modus ponens and modus tollens for the compositional rule of inference with aggregation functions",
  "authors": [
    "Dechao Li",
    "Qingxue Zeng"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2112.12808",
  "categories": [
    "math.LO",
    "cs.AI"
  ],
  "abstract": "The compositional rule of inference (CRI) proposed by Zadeh has been widely applied in artificial intelligence, control, data mining, image processing, decision making and so on. Recently, Li and Zeng [Li, D., Zeng, Q. Approximate reasoning with aggregation functions satisfying GMP rules, Artificial Intelligence Review (2022), https://doi.org/10.1007/s10462-022-10136-1] shown an A-compositional rule of inference (ACRI) method in which generalizes the t-norm to any aggregation function in CRI method and studied its validity using GMP rules. In this paper, we continue to investigate the validity of ACRI method from a logical view and an interpolative view. Specifically, to discuss the modus ponens (MP) and modus tollens (MT) properties of ACRI method based on well-known fuzzy implications with aggregation functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-03T01:55:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modus tollens",
      "modus ponens",
      "compositional rule",
      "acri method",
      "aggregation functions satisfying gmp rules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}