"valuation function" meaning in English

{
  "forms": [
    {
      "form": "valuation functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "valuation function (plural valuation functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "Say that a model's interpration assigns true to A and false to B. Then the valuation function assigns false to \"not A\", true to \"not B\", false to \"A implies B\", false to \"A and B\", and true to \"A or B\"."
        }
      ],
      "glosses": [
        "A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective."
      ],
      "id": "en-valuation_function-en-noun-t9hlSs00",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "function",
          "function"
        ],
        [
          "truth value",
          "truth value"
        ],
        [
          "well-formed formula",
          "well-formed formula"
        ],
        [
          "model",
          "model"
        ],
        [
          "propositions",
          "propositions"
        ],
        [
          "recursively",
          "recursively"
        ],
        [
          "connective",
          "connective"
        ]
      ],
      "raw_glosses": [
        "(logic) A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ]
    }
  ],
  "word": "valuation function"
}

{
  "forms": [
    {
      "form": "valuation functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "valuation function (plural valuation functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Logic"
      ],
      "examples": [
        {
          "text": "Say that a model's interpration assigns true to A and false to B. Then the valuation function assigns false to \"not A\", true to \"not B\", false to \"A implies B\", false to \"A and B\", and true to \"A or B\"."
        }
      ],
      "glosses": [
        "A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "function",
          "function"
        ],
        [
          "truth value",
          "truth value"
        ],
        [
          "well-formed formula",
          "well-formed formula"
        ],
        [
          "model",
          "model"
        ],
        [
          "propositions",
          "propositions"
        ],
        [
          "recursively",
          "recursively"
        ],
        [
          "connective",
          "connective"
        ]
      ],
      "raw_glosses": [
        "(logic) A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ]
    }
  ],
  "word": "valuation function"
}