"formal system" meaning in English

{
  "forms": [
    {
      "form": "formal systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "formal system (plural formal systems)",
      "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": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Japanese terms with redundant script codes",
          "parents": [
            "Terms with redundant script codes",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Dutch translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Greek translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Japanese translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Persian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The grouping of a formal language and a set of inference rules and/or axioms."
      ],
      "id": "en-formal_system-en-noun-vEbCJM3T",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "formal language",
          "formal language"
        ],
        [
          "inference rule",
          "inference rule"
        ],
        [
          "axiom",
          "axiom"
        ]
      ],
      "meronyms": [
        {
          "word": "formal language"
        },
        {
          "word": "axiom"
        },
        {
          "word": "inference rule"
        },
        {
          "word": "theory"
        },
        {
          "word": "syntax"
        },
        {
          "word": "semantics"
        }
      ],
      "raw_glosses": [
        "(logic) The grouping of a formal language and a set of inference rules and/or axioms."
      ],
      "synonyms": [
        {
          "word": "logical system"
        },
        {
          "word": "logical calculus"
        },
        {
          "word": "logic"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "translations": [
        {
          "code": "nl",
          "lang": "Dutch",
          "sense": "combination of formal language and inference rules",
          "tags": [
            "neuter"
          ],
          "word": "formeel systeem"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "combination of formal language and inference rules",
          "tags": [
            "neuter"
          ],
          "word": "formales System"
        },
        {
          "code": "el",
          "lang": "Greek",
          "roman": "typikó sýstima",
          "sense": "combination of formal language and inference rules",
          "tags": [
            "neuter"
          ],
          "word": "τυπικό σύστημα"
        },
        {
          "alt": "けいしきてきたいけい",
          "code": "ja",
          "lang": "Japanese",
          "roman": "keishiki-teki-taikei",
          "sense": "combination of formal language and inference rules",
          "word": "形式的体系"
        },
        {
          "alt": "けいしきたいけい",
          "code": "ja",
          "lang": "Japanese",
          "roman": "keishiki-taikei",
          "sense": "combination of formal language and inference rules",
          "word": "形式体系"
        },
        {
          "code": "fa",
          "lang": "Persian",
          "sense": "combination of formal language and inference rules",
          "word": "سیستم صوری"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "formalʹnaja sistéma",
          "sense": "combination of formal language and inference rules",
          "word": "формальная систе́ма"
        }
      ],
      "wikipedia": [
        "formal system"
      ]
    }
  ],
  "word": "formal system"
}

{
  "forms": [
    {
      "form": "formal systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "formal system (plural formal systems)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "word": "formal language"
    },
    {
      "word": "axiom"
    },
    {
      "word": "inference rule"
    },
    {
      "word": "theory"
    },
    {
      "word": "syntax"
    },
    {
      "word": "semantics"
    }
  ],
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Japanese terms with redundant script codes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Dutch translations",
        "Terms with German translations",
        "Terms with Greek translations",
        "Terms with Japanese translations",
        "Terms with Persian translations",
        "Terms with Russian translations",
        "en:Logic"
      ],
      "glosses": [
        "The grouping of a formal language and a set of inference rules and/or axioms."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "formal language",
          "formal language"
        ],
        [
          "inference rule",
          "inference rule"
        ],
        [
          "axiom",
          "axiom"
        ]
      ],
      "raw_glosses": [
        "(logic) The grouping of a formal language and a set of inference rules and/or axioms."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "formal system"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "logical system"
    },
    {
      "word": "logical calculus"
    },
    {
      "word": "logic"
    }
  ],
  "translations": [
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "combination of formal language and inference rules",
      "tags": [
        "neuter"
      ],
      "word": "formeel systeem"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "combination of formal language and inference rules",
      "tags": [
        "neuter"
      ],
      "word": "formales System"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "typikó sýstima",
      "sense": "combination of formal language and inference rules",
      "tags": [
        "neuter"
      ],
      "word": "τυπικό σύστημα"
    },
    {
      "alt": "けいしきてきたいけい",
      "code": "ja",
      "lang": "Japanese",
      "roman": "keishiki-teki-taikei",
      "sense": "combination of formal language and inference rules",
      "word": "形式的体系"
    },
    {
      "alt": "けいしきたいけい",
      "code": "ja",
      "lang": "Japanese",
      "roman": "keishiki-taikei",
      "sense": "combination of formal language and inference rules",
      "word": "形式体系"
    },
    {
      "code": "fa",
      "lang": "Persian",
      "sense": "combination of formal language and inference rules",
      "word": "سیستم صوری"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "formalʹnaja sistéma",
      "sense": "combination of formal language and inference rules",
      "word": "формальная систе́ма"
    }
  ],
  "word": "formal system"
}