"Kripke model" meaning in English

{
  "etymology_text": "Named after Saul Kripke.",
  "forms": [
    {
      "form": "Kripke models",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Kripke model (plural Kripke models)",
      "name": "en-noun"
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "A formula is intuitionistically valid iff it is forced true by every world of every Kripke model."
        },
        {
          "text": "A terminal world of a Kripke model (for intuitionistic logic) has a forcing relation equivalent to a classical model/interpretation."
        },
        {
          "text": "If a given world (in a Kripke model (for intuitionistic logic)) forces neither A nor ¬A then there is some possible \"future\" world (accessible from the \"present\" one) in which A is forced true. In particular, if A eventually becomes forced somewhere along any possible time thread (towards the \"future\"), then the present world would force ¬¬A to be true, but if this does not happen there there exists some possible future world in which ¬A becomes true."
        }
      ],
      "glosses": [
        "A Kripke frame together with either one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are \"true\" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is \"true\", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p."
      ],
      "id": "en-Kripke_model-en-noun-~yupOtQQ",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "Kripke frame",
          "Kripke frame"
        ],
        [
          "prime formula",
          "prime formula"
        ],
        [
          "modal logic",
          "modal logic"
        ],
        [
          "intuitionistic logic",
          "intuitionistic logic"
        ]
      ],
      "raw_glosses": [
        "(logic) A Kripke frame together with either one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are \"true\" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is \"true\", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p."
      ],
      "related": [
        {
          "word": "Kripke semantics"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Kripke semantics",
        "Saul Kripke"
      ]
    }
  ],
  "word": "Kripke model"
}

{
  "etymology_text": "Named after Saul Kripke.",
  "forms": [
    {
      "form": "Kripke models",
      "tags": [
        "plural"
      ]
    }
  ],
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    {
      "args": {},
      "expansion": "Kripke model (plural Kripke models)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Kripke semantics"
    }
  ],
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    {
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        "English countable nouns",
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      "examples": [
        {
          "text": "A formula is intuitionistically valid iff it is forced true by every world of every Kripke model."
        },
        {
          "text": "A terminal world of a Kripke model (for intuitionistic logic) has a forcing relation equivalent to a classical model/interpretation."
        },
        {
          "text": "If a given world (in a Kripke model (for intuitionistic logic)) forces neither A nor ¬A then there is some possible \"future\" world (accessible from the \"present\" one) in which A is forced true. In particular, if A eventually becomes forced somewhere along any possible time thread (towards the \"future\"), then the present world would force ¬¬A to be true, but if this does not happen there there exists some possible future world in which ¬A becomes true."
        }
      ],
      "glosses": [
        "A Kripke frame together with either one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are \"true\" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is \"true\", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "Kripke frame",
          "Kripke frame"
        ],
        [
          "prime formula",
          "prime formula"
        ],
        [
          "modal logic",
          "modal logic"
        ],
        [
          "intuitionistic logic",
          "intuitionistic logic"
        ]
      ],
      "raw_glosses": [
        "(logic) A Kripke frame together with either one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are \"true\" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is \"true\", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Kripke semantics",
        "Saul Kripke"
      ]
    }
  ],
  "word": "Kripke model"
}