{"query": "Formal logic", "count": 20, "results": [{"id": "card_instr_formal_logic", "title": "Formal logic", "shelf": "codex", "surface": "secular", "snippet": "The Formal logic verifier (src/concordance/verifiers/formal_logic.py). Builds on: Boolean algebra — the base of logic. Found from the code's own imports, never invented; the module keeps the logic, th", "authority_tier": "engine_derived", "source": "verifier: formal_logic", "readable": false, "generated": false}, {"id": "card_src_word_formal_logic", "title": "formal logic", "shelf": "dictionary", "surface": "secular", "snippet": "formal logic: (noun) any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity — syn: symbolic logic, mathema", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_theory_g_del_s_incompleteness_theorems", "title": "Gödel's incompleteness theorems", "shelf": "theories", "surface": "secular", "snippet": "Gödel's incompleteness theorems — an engine domain that can touch it: formal_logic. Calibration: map-only — a meta-theorem about systems, not a sealable computation. FIRST (1931): any consistent forma", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_boolean_algebra_propositional_logic", "title": "Boolean algebra / propositional logic", "shelf": "theories", "surface": "secular", "snippet": "Boolean algebra / propositional logic — an engine domain that can touch it: formal_logic. Calibration: seals. Two values and three operations — AND, OR, NOT — with laws of their own (De Morgan's, dist", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_zermelo_fraenkel_set_theory_zfc", "title": "Zermelo–Fraenkel set theory (ZFC)", "shelf": "theories", "surface": "secular", "snippet": "Zermelo–Fraenkel set theory (ZFC) — an engine domain that can touch it: formal_logic. Calibration: map-only — an axiomatic foundation, not a computation. Nine or so axioms about sets from which essent", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_formal_logic_epistemology", "title": "Formal logic & epistemology (validity, inference)", "shelf": "theories", "surface": "secular", "snippet": "Formal logic & epistemology (validity, inference) — an engine domain that can touch it: philosophy. Calibration: map-only — validity checks compute; epistemology is interpretive. VALIDITY and TRUTH ar", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_boolean_algebra_propositional_logic__formal_logic_epistemology", "title": "Bridge: Boolean algebra / propositional logic  ↔  Formal logic & epistemology (validity, inference)", "shelf": "bridges", "surface": "secular", "snippet": "Boolean algebra / propositional logic and Formal logic & epistemology (validity, inference) are the same form in different domains. Boole's algebra IS propositional inference in arithmetic dress: AND/", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_toulmin_argument__formal_logic_epistemology", "title": "Bridge: The Toulmin model of argumentation  ↔  Formal logic & epistemology (validity, inference)", "shelf": "bridges", "surface": "secular", "snippet": "The Toulmin model of argumentation and Formal logic & epistemology (validity, inference) are the same form in different domains. the warrant is the informal cousin of a logical inference rule — argume", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_theory_income_capitalization", "title": "Income capitalization (V = NOI / cap rate)", "shelf": "theories", "surface": "secular", "snippet": "Income capitalization (V = NOI / cap rate) — an engine domain that can touch it: real_estate. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and sea", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_v_f4b827f56b3c", "title": "p ∨ ¬p is a tautology · ¬(p ∧ q) ≡ ¬p ∨ ¬q  (De Morgan)", "shelf": "formal_logic", "surface": "secular", "snippet": "Verdict: HOLDS.\n• formal_logic.tautology: formula 'p | ~p' tautology=True, matches claim\n• formal_logic.equivalence: '~(p & q)' ≡ '~p | ~q' = True, matches claim\nSealed and independently re-checkable:", "authority_tier": "engine", "source": "Verified by the engine — formal_logic", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_tautology", "title": "Formal Logic: tautology", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: tautology.\n\nGIVEN\n  conclusion = q\n  formula = p & q\n\nCLAIMED\n  claimed_tautology = False\n\nTHE ENGINE'S VERDICT\n  formal_logic.tautology: CONFIRMED — formula 'p & q' ta", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_calc_v_formal_logic_tautology", "title": "Tautology", "shelf": "calculations", "surface": "secular", "snippet": "Tautology — formal_logic. Formula: phi true under every assignment. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.tautology — the deterministic check the", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_works_logic", "title": "Two laws of thought, checked over every case", "shelf": "the-works", "surface": "secular", "snippet": "The law of excluded middle (p or not-p is always true) and De Morgan's law are verified across the entire truth table — not argued, exhaustively decided.  Worked & sealed by the engine — p ∨ ¬p is a t", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_equivalent", "title": "Formal Logic: equivalent", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: equivalent.\n\nGIVEN\n  conclusion = q\n  formula_a = p | q\n  formula_b = ~(~p & ~q)\n\nCLAIMED\n  claimed_equivalent = True\n\nTHE ENGINE'S VERDICT\n  formal_logic.equivalence: ", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_entailment", "title": "Formal Logic: entailment", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: entailment.\n\nGIVEN\n  conclusion = q\n  premises = [p, p >> q]\n\nCLAIMED\n  claimed_entailment = True\n\nTHE ENGINE'S VERDICT\n  formal_logic.entailment: CONFIRMED — premises ", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_contradiction", "title": "Formal Logic: contradiction", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: contradiction.\n\nGIVEN\n  conclusion = q\n  formula = p & q\n\nCLAIMED\n  claimed_contradiction = False\n\nTHE ENGINE'S VERDICT\n  formal_logic.contradiction: CONFIRMED — formul", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_satisfiable", "title": "Formal Logic: satisfiable", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: satisfiable.\n\nGIVEN\n  conclusion = q\n  formula = p & q\n\nCLAIMED\n  claimed_satisfiable = True\n\nTHE ENGINE'S VERDICT\n  formal_logic.satisfiability: CONFIRMED — formula 'p", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_spine_domain_formal_logic", "title": "Formal Logic — what this engine can check", "shelf": "formal_logic", "surface": "secular", "snippet": "The formal logic shelf of the keeping. This engine holds a deterministic verifier for formal logic: hand it a claim in the LOGIC_VERIFY shape and it returns a verdict, the worked trail, and a re-check", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_calc_v_formal_logic_equivalence", "title": "Equivalence", "shelf": "calculations", "surface": "secular", "snippet": "Equivalence — formal_logic. Formula: A <=> B (same truth table). Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.equivalence — the deterministic check the ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_formal_logic_entailment", "title": "Entailment", "shelf": "calculations", "surface": "secular", "snippet": "Entailment — formal_logic. Formula: A |= B (every model of A models B). Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.entailment — the deterministic chec", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_instr_formal_logic"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}