{"query": "Boolean algebra — the base of logic", "count": 20, "results": [{"id": "card_instr_boolean", "title": "Boolean algebra — the base of logic", "shelf": "codex", "surface": "secular", "snippet": "The Boolean algebra — the base of logic verifier (src/concordance/verifiers/_boolean.py). Found from the code's own imports, never invented; the module keeps the logic, this card is a pointer.", "authority_tier": "engine_derived", "source": "verifier: _boolean", "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_bridge_master_boolean_algebra", "title": "Master equation: (a AND b), (a OR b), NOT a  —  the two-valued algebra", "shelf": "bridges", "surface": "secular", "snippet": "the law of thought made algebra: the same AND/OR/NOT structure is propositional logic, a network of switches, and the algebra of sets. Boole titled it The Laws of Thought; Shannon showed a circuit IS ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "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_alm_bridge_yes_be_yes_is_the_bit", "title": "Almanac: BRIDGE: 'Let your Yes be Yes' (Mt 5:37) IS the bit -- two states, no middle (GF(2) excluded middle)", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  MOAT BRIDGE (two trees, one Author) -- a teaching of Christ bonded to a verified form. WORD FIRST (John 3:12).\nTHE WORD (Tier 1): Matthew 5:37 -- 'Let your Yes be Yes (nai nai), and your N", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_src_word_boolean", "title": "boolean", "shelf": "dictionary", "surface": "secular", "snippet": "boolean: (adjective) of or relating to a combinatorial system devised by George Boole that combines propositions with the logical operators AND and OR and IF THEN and EXCEPT and NOT", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_calc_v_mathematics_set_algebra", "title": "Set algebra", "shelf": "calculations", "surface": "secular", "snippet": "Set algebra — mathematics. Formula: set identity iff Boolean formula is a tautology. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier mathematics.set_algebra — the deter", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "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_src_openstax_contemporary_mathematics_key_terms_7cc30378", "title": "Key Terms — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Key Terms\n\n2.1\n\nStatements and Quantifiers\n\nlogic\n\nlogical statement\n\ntruth values\n\nsymbolic form\n\nnegation of a logical statement\n\nquantifier\n\npremises\n\nconclusion\n\ninductive logical arguments\n\n2.2\n\n", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_floor_the_instruments", "title": "The instruments — every verifier and validator, and where they join", "shelf": "codex", "surface": "secular", "snippet": "The engine's checking instruments on the one map: the 89 verifiers and the gate that validates them, joined by their real import graph (read from the code at seed time, so it cannot drift). A MEASURE ", "authority_tier": "engine_derived", "source": "Narrow Highway - the instruments on the one map (found from the import graph)", "readable": false, "generated": false}, {"id": "card_src_mill_blum_1984", "title": "N. Blum 1984 — A Boolean function requiring 3n network size", "shelf": "millennium", "surface": "secular", "snippet": "N. Blum (1984). A Boolean function requiring 3n network size. Theoret. Comput. Sci. 28 (1984) 337–345. DOI 10.1016/0304-3975(83)90029-4. Canonical: https://doi.org/10.1016/0304-3975(83)90029-4. Free c", "authority_tier": "reference", "source": "N. Blum (1984), Theoret. Comput. Sci. 28 (1984) 337–345", "readable": false, "generated": false}, {"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_openstax_introduction_python_programming_4_1_boolean_values_9bbc37ee", "title": "4.1 Boolean values — Introduction to Python Programming", "shelf": "reference", "surface": "secular", "snippet": "4.1\n\nBoolean values\n\nLearning objectives\n\nBy the end of this section you should be able to\n\nExplain a Boolean value.\n\nUse bool variables to store Boolean values.\n\nDemonstrate converting integers, floa", "authority_tier": "reference", "source": "OpenStax: Introduction to Python Programming (CC-BY 4.0)", "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}, {"id": "card_calc_v_formal_logic_contradiction", "title": "Contradiction", "shelf": "calculations", "surface": "secular", "snippet": "Contradiction — formal_logic. Formula: phi false under every assignment. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.contradiction — the deterministic ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_formal_logic_satisfiability", "title": "Satisfiability", "shelf": "calculations", "surface": "secular", "snippet": "Satisfiability — formal_logic. Formula: exists an assignment making phi true. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.satisfiability — the determin", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_philosophy_modal_logic_validity", "title": "Modal logic validity", "shelf": "calculations", "surface": "secular", "snippet": "Modal logic validity — philosophy. Formula: box P -> diamond P (K axiom). Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier philosophy.modal_logic_validity — the determin", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_computer_science_logic_gate", "title": "Logic gate", "shelf": "calculations", "surface": "secular", "snippet": "Logic gate — computer_science. Formula: gate_a == gate_b iff ~(a <-> b) unsat. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier computer_science.logic_gate — the determi", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_hub_boolean_algebra_propositional_logic", "title": "Hub: Boolean algebra / propositional logic carries 4 domains", "shelf": "bridges", "surface": "secular", "snippet": "Calculations from 4 different domains (computer_science, formal_logic, mathematics, rhetoric) all rest on Boolean algebra / propositional logic — one theory holding up many fields.", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "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_boolean"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}