Regla de entrada: (socio OR invitado) AND NOT vetado, comprobada de todas las formas
Una regla de acceso, (member OR invited) AND NOT banned, pasada por todas las herramientas: la tabla de verdad de ocho filas, las tres comprobaciones exactas, el simplificador, las dos formas normales, los recuentos de compuertas NAND y NOR y un mapa de Karnaugh.
La regla tiene tres entradas. member significa que la persona es socia, invited que tiene invitación y banned que está vetada. Se permite la entrada cuando al menos una de las dos primeras es verdadera y la tercera es falsa. La lectura en lenguaje llano del motor dice lo mismo: allow_entry es verdadero exactamente cuando se cumple al menos uno entre member e invited y banned es falso. Con tres entradas la tabla de verdad tiene ocho filas, y la salida es verdadera en tres de ellas: Σm(2, 4, 6) en notación de mintérminos.
La comprobación de tautología se viola, con el contraejemplo member = FALSO, invited = FALSO, banned = FALSO; la de contradicción se viola y la satisfacibilidad se cumple, con el testigo member = FALSO, invited = VERDADERO, banned = FALSO. El simplificador no encontró ninguna ley que acorte la expresión: se queda en tres operadores. La FNC es la propia regla, dos cláusulas; la FND, con un paso de distributividad, es (member AND NOT banned) OR (invited AND NOT banned), que es lo que deriva el mapa de Karnaugh con dos implicantes primos. La forma solo con NOR necesita 2 compuertas, NOR(NOR(member, invited), banned); la forma solo con NAND, 11.
Esta forma, un OR de maneras de entrar seguido de un AND con un bloqueo, es la regla de acceso más común en software: una cláusula de guarda, una puerta de funcionalidad, una comprobación de socio. Lo que hay que vigilar es la agrupación. El OR debe evaluarse antes de aplicar la condición NOT banned; si no, los socios vetados entran, que es justo lo que la página del error compañera muestra fila por fila. Al exportar la regla a Python o SQL los paréntesis viajan con ella, y la tabla de ocho filas es el oráculo de prueba de cualquier reimplementación.
member: la persona es socia; invited: la persona tiene invitación; banned: la persona está vetada;
allow_entry := (member OR invited) AND NOT banned · salida
Comprobaciones exactas
Tabla de verdad (8 filas)
| # | member | invited | banned | allow_entry |
|---|---|---|---|---|
| 0 | FALSO | FALSO | FALSO | FALSO |
| 1 | FALSO | FALSO | VERDADERO | FALSO |
| 2 | FALSO | VERDADERO | FALSO | VERDADERO |
| 3 | FALSO | VERDADERO | VERDADERO | FALSO |
| 4 | VERDADERO | FALSO | FALSO | VERDADERO |
| 5 | VERDADERO | FALSO | VERDADERO | FALSO |
| 6 | VERDADERO | VERDADERO | FALSO | VERDADERO |
| 7 | VERDADERO | VERDADERO | VERDADERO | FALSO |
Lectura en lenguaje claro
Principianteallow_entry es verdadero exactamente cuando se cumplen las dos condiciones siguientes:
1. al menos uno entre member e invited es verdadero (pueden serlo ambos)
2. banned es falso
En todos los demás casos, allow_entry es falso.
Sobre los operadores:
- AND (Y) solo es verdadero cuando todas sus partes son verdaderas.
- OR (O) es inclusivo: es verdadero en cuanto al menos una parte es verdadera, también cuando lo son varias.
- NOT (NO) invierte un valor: lo verdadero pasa a ser falso y lo falso, verdadero.
Intermedioallow_entry es verdadero exactamente cuando se cumplen las dos condiciones siguientes:
1. al menos uno entre member e invited es verdadero (pueden serlo ambos)
2. banned es falso
En todos los demás casos, allow_entry es falso.
Avanzadoallow_entry es verdadero exactamente cuando se cumplen las dos condiciones siguientes [conjunción ∧]:
1. al menos uno entre member e invited es verdadero (pueden serlo ambos) [disyunción inclusiva ∨]
2. banned es falso [negación ¬]
En todos los demás casos, allow_entry es falso.
Notación formal: (member ∨ invited) ∧ ¬banned
Diagrama lógico
Simplificación paso a paso
El motor no encontró ninguna ley que acorte esta expresión; ya es tan corta como sus leyes de reescritura permiten.
(member OR invited) AND NOT banned
Mapa de Karnaugh
- celdas m4, m6
member AND NOT banned - celdas m2, m6
invited AND NOT banned
Mintérminos y maxtérminos
allow_entry(member, invited, banned) = Σm(2, 4, 6)allow_entry(member, invited, banned) = ΠM(0, 1, 3, 5, 7)Orden de variables: member, invited, banned · 8 filas
Formas normales
Forma normal conjuntiva (FNC)
(member OR invited) AND NOT banned2 cláusulas, 3 literales · complete
Forma normal disyuntiva (FND)
(member AND NOT banned) OR (invited AND NOT banned)2 términos, 4 literales · complete · Distributividad ×1
Solo NAND, solo NOR
Forma solo con NAND
NAND(NAND(NAND(NAND(member, member), NAND(invited, invited)), NAND(banned, banned)), NAND(NAND(NAND(member, member), NAND(invited, invited)), NAND(banned, banned)))11 compuertas · equivalencia verificada en todas las filas
Forma solo con NOR
NOR(NOR(member, invited), banned)2 compuertas · equivalencia verificada en todas las filas
La misma regla como código
Python
# -*- coding: utf-8 -*-
# Generated by Tangibool (tangibool.python/1). Do not edit by hand; regenerate from the source revision.
# Model: not stated
# Source revision: reference
# Interpretation status: not stated
"""Tangibool evaluator (decision model).
Generated deterministically from the validated Boolean model; it evaluates exactly that
model. It does not establish that the model is a complete, legal, or safe statement of a
real-world rule, and evaluating examples does not verify the rule.
Source revision: reference
Interpretation status: not stated
Exporter: 1.0.0 (format tangibool.python/1; engine 1.0.0; semantics tangibool-semantics/1)
Logic digest: f0daa82174670c788f59eb058d07f7601cd0ace4ed94d61a747cc26c41fd4e0d
Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
Inputs (dict keys, declared order) and generated parameter names:
'member' -> input_member
'invited' -> input_invited
'banned' -> input_banned
Outputs (declared order) and their functions:
'allow_entry' -> output_allow_entry(inputs)
Assumptions (the declared scope, checked by in_scope(inputs)):
none; every complete assignment is in scope.
Input contract:
Every required input must be exactly True or False (type(value) is bool). Missing
inputs, None, strings, integers (including 0 and 1), and keys that are not declared
inputs raise InputError before anything is evaluated, including inputs that a
short-circuiting operator would never read. Results are always bool.
Scope:
Decision functions raise OutOfScopeError when the inputs violate an assumption; an
out-of-scope assignment is never turned into a False result. Pass check_scope=False
to evaluate without the scope check, and use in_scope(inputs) to test it separately.
Usage:
import tangibool_model as model
model.evaluate({'member': False, 'invited': False, 'banned': False})
# -> {'allow_entry': False}
model.output_allow_entry({'member': False, 'invited': False, 'banned': False})
# -> False
model.evaluate({'member': 1, 'invited': False, 'banned': False})
# raises InputError: 1 is an int, not a bool
"""
import collections.abc as _abc
from typing import Dict, Mapping, Tuple
__all__ = [
"MODEL_INFO",
"IDENTIFIER_MAP",
"INPUT_NAMES",
"OUTPUT_NAMES",
"ASSUMPTIONS",
"InputError",
"OutOfScopeError",
"minterm_index",
"in_scope",
"evaluate",
"output_allow_entry",
]
MODEL_INFO = {
"format": "tangibool.python/1",
"mode": "decision",
"model": None,
"revision": "reference",
"interpretation": None,
"exporter": "1.0.0",
"engine_version": "1.0.0",
"semantics_version": "tangibool-semantics/1",
"logic_digest": "f0daa82174670c788f59eb058d07f7601cd0ace4ed94d61a747cc26c41fd4e0d",
"assumptions_digest": "d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78",
"primary_output": "allow_entry",
"unused_inputs": (),
"subcircuits": (),
}
# Stable ID -> generated identifier (reversible mapping; names are exact, escaped strings).
IDENTIFIER_MAP = {
"v_79df34978043": {"kind": "input", "name": "member", "identifier": "input_member"},
"v_8afde06f51e3": {"kind": "input", "name": "invited", "identifier": "input_invited"},
"v_60b2536f5dc8": {"kind": "input", "name": "banned", "identifier": "input_banned"},
"f_ae8686d89791": {"kind": "output", "name": "allow_entry", "identifier": "output_allow_entry"},
}
INPUT_NAMES = ("member", "invited", "banned")
OUTPUT_NAMES = ("allow_entry",)
ASSUMPTIONS = ()
_DECLARED_INPUTS = frozenset(INPUT_NAMES)
_SCOPE_INPUTS = ()
_ASSUMPTION_FORMULAS = {entry["name"]: entry["formula"] for entry in ASSUMPTIONS}
class InputError(ValueError):
"""Raised when inputs are missing, undeclared, or not exactly True/False.
Every required input must satisfy type(value) is bool. Missing inputs, None, strings,
integers (including 0 and 1), and keys that are not declared inputs are rejected before
anything is evaluated. A missing input is never treated as False. The individual problems
are listed in the problems attribute.
"""
def __init__(self, problems):
self.problems = tuple(problems)
super().__init__("Invalid inputs: " + "; ".join(self.problems))
class OutOfScopeError(ValueError):
"""Raised when the inputs violate the model's assumptions (its declared scope).
Outside its assumptions the rule has no decision: this error is never a False result.
The names of the violated assumptions are in the violated attribute.
"""
def __init__(self, violated):
self.violated = tuple(violated)
details = ", ".join(name + " (" + _ASSUMPTION_FORMULAS.get(name, "?") + ")" for name in self.violated)
super().__init__(
"Out of scope: the inputs violate "
+ ("assumption " if len(self.violated) == 1 else "assumptions ")
+ details
+ ". The rule has no decision outside its assumptions; this is not a False result."
)
def _short_repr(value: object) -> str:
text = repr(value)
return text if len(text) <= 60 else text[:57] + "..."
def _checked_inputs(inputs: Mapping[str, bool], required: Tuple[str, ...], check_scope: bool) -> Dict[str, bool]:
"""Validate inputs strictly before anything is evaluated and return a plain copy."""
if type(check_scope) is not bool:
raise TypeError("check_scope must be True or False")
if not isinstance(inputs, _abc.Mapping):
raise InputError(["inputs must be a mapping from input names to True/False, got " + type(inputs).__name__])
problems = []
for key in inputs:
if type(key) is not str or key not in _DECLARED_INPUTS:
declared = ", ".join(repr(name) for name in INPUT_NAMES) or "none"
problems.append("undeclared input " + _short_repr(key) + " (declared inputs: " + declared + ")")
needed = tuple(required) + (_SCOPE_INPUTS if check_scope else ())
for name in needed:
if name not in inputs:
problems.append("missing required input " + repr(name))
for key, value in inputs.items():
if type(key) is str and key in _DECLARED_INPUTS and type(value) is not bool:
problems.append(
"input " + repr(key) + " must be True or False (type bool), got "
+ type(value).__name__ + " " + _short_repr(value)
)
if problems:
raise InputError(list(dict.fromkeys(problems)))
return dict(inputs.items())
def _require_bool_args(function: str, pairs: Tuple[Tuple[str, object], ...]) -> None:
problems = [
"argument " + repr(name) + " of " + function + " must be True or False (type bool), got "
+ type(value).__name__ + " " + _short_repr(value)
for name, value in pairs
if type(value) is not bool
]
if problems:
raise InputError(problems)
def minterm_index(*values: bool) -> int:
"""Row index of an assignment over a declared variable order.
The first value is the most significant bit, so all-False is row 0. Used for indexed
minterm (sum) and maxterm (product) forms.
"""
index = 0
for value in values:
if type(value) is not bool:
raise InputError(["minterm_index() takes True/False values, got " + type(value).__name__ + " " + _short_repr(value)])
index = index * 2 + (1 if value else 0)
return index
def _scope_values(values: Dict[str, bool]) -> Tuple[Tuple[str, bool], ...]:
"""Value of every enabled, confirmed assumption for validated inputs, in declared order."""
return ()
def _require_in_scope(values: Dict[str, bool]) -> None:
violated = tuple(name for name, holds in _scope_values(values) if not holds)
if violated:
raise OutOfScopeError(violated)
def in_scope(inputs: Mapping[str, bool]) -> bool:
"""True when the inputs satisfy every assumption (the model's declared scope).
Requires the inputs the assumptions read; raises InputError for invalid inputs.
"""
values = _checked_inputs(inputs, (), True)
return all(holds for _, holds in _scope_values(values))
# ---- Formula bodies (inputs are validated by the public functions below) ----
def _compute_output_allow_entry(input_member: bool, input_invited: bool, input_banned: bool) -> bool:
"""Decision output 'allow_entry': (member OR invited) AND NOT banned"""
return (input_member or input_invited) and (not input_banned)
# ---- Public API ----
def output_allow_entry(inputs: Mapping[str, bool], *, check_scope: bool = True) -> bool:
"""Decision output 'allow_entry' (stable ID f_ae8686d89791).
'allow_entry' := (member OR invited) AND NOT banned
Required inputs: 'member', 'invited', 'banned'.
Raises InputError for missing, undeclared, or non-bool inputs, and OutOfScopeError
when check_scope is True and the inputs violate an assumption.
"""
values = _checked_inputs(inputs, ("member", "invited", "banned"), check_scope)
if check_scope:
_require_in_scope(values)
output_allow_entry_value = _compute_output_allow_entry(values["member"], values["invited"], values["banned"])
return output_allow_entry_value
def evaluate(inputs: Mapping[str, bool], *, check_scope: bool = True) -> Dict[str, bool]:
"""Evaluate every output (declared order); each output is computed once.
Required inputs: 'member', 'invited', 'banned'.
Raises InputError for missing, undeclared, or non-bool inputs, and OutOfScopeError
when check_scope is True and the inputs violate an assumption.
"""
values = _checked_inputs(inputs, ("member", "invited", "banned"), check_scope)
if check_scope:
_require_in_scope(values)
output_allow_entry_value = _compute_output_allow_entry(values["member"], values["invited"], values["banned"])
return {
"allow_entry": output_allow_entry_value,
}
PostgreSQL
-- Tangibool PostgreSQL export (tangibool.postgresql/1)
-- Target: PostgreSQL 16 or later with typed boolean inputs; tested with PostgreSQL 18.3 (PGlite 0.5.8).
-- Not a claim of compatibility with other SQL dialects.
-- Model: not stated
-- Source revision: reference
-- Interpretation status: not stated
-- Exporter: 1.0.0 (engine 1.0.0; semantics tangibool-semantics/1)
-- Logic digest: f0daa82174670c788f59eb058d07f7601cd0ace4ed94d61a747cc26c41fd4e0d
-- Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
-- Mode: decision
--
-- Read-only: this file contains only WITH / VALUES / SELECT statements. No DDL, DML,
-- procedures, credentials, network access, or database changes. The expressions are pure
-- Boolean expressions, so their result does not depend on SQL evaluation order.
--
-- NON-NULL INPUT PRECONDITION: NULL is not a truth value of this rule. Every fragment below
-- is defined only when every input column it reads is a non-NULL boolean. The guard template
-- (section 2) marks any NULL input as 'invalid_input' and any row that violates the
-- assumptions as 'out_of_scope', and fills output columns only for 'ok' rows; a NULL in an
-- output column of another row is an envelope marker, not a third truth value. Never wrap
-- the fragments in COALESCE(..., FALSE) or otherwise choose a meaning for unknown inputs.
-- This evaluates the supplied model; it does not show that the model is a complete, legal,
-- or safe statement of a real-world rule.
--
-- Input columns (stable ID: name -> column):
-- v_79df34978043: member -> "in_member"
-- v_8afde06f51e3: invited -> "in_invited"
-- v_60b2536f5dc8: banned -> "in_banned"
-- Output columns:
-- f_ae8686d89791: allow_entry -> "out_allow_entry"
-- Assumptions (scope K; exported separately and never folded into an output):
-- none; every complete input row is in scope.
-- ----------------------------------------------------------------------------------------------
-- 1. Expression fragments (parenthesised; non-NULL boolean inputs required)
-- ----------------------------------------------------------------------------------------------
--
-- [out_allow_entry] output allow_entry (stable ID f_ae8686d89791)
-- allow_entry := (member OR invited) AND NOT banned
-- PRECONDITION: "in_member", "in_invited", "in_banned" are non-NULL booleans.
-- (("in_member" OR "in_invited") AND (NOT "in_banned"))
--
-- ----------------------------------------------------------------------------------------------
-- 2. Guard template (read-only SELECT over an inputs list)
-- ----------------------------------------------------------------------------------------------
-- Replace the example rows between the markers with your own rows, or replace the inputs
-- CTE with a SELECT that provides the boolean columns listed in the header. status is
-- 'invalid_input' when any input is NULL, 'out_of_scope' when the assumptions are false, and
-- 'ok' otherwise; output columns are filled only for 'ok' rows (NULL elsewhere is an
-- envelope marker). Assumption columns are shown for rows with complete inputs.
WITH inputs ("row_id", "in_member", "in_invited", "in_banned") AS (
-- tangibool:example-rows:begin
VALUES
(1, FALSE, FALSE, FALSE),
(2, FALSE, FALSE, TRUE),
(3, FALSE, TRUE, FALSE),
(4, FALSE, TRUE, TRUE),
(5, TRUE, FALSE, FALSE),
(6, TRUE, FALSE, TRUE),
(7, TRUE, TRUE, FALSE),
(8, TRUE, TRUE, TRUE),
(9, NULL::boolean, FALSE, FALSE)
-- tangibool:example-rows:end
),
checked AS (
SELECT
inputs.*,
CASE
WHEN "in_member" IS NULL OR "in_invited" IS NULL OR "in_banned" IS NULL THEN 'invalid_input'
ELSE 'ok'
END AS "status"
FROM inputs
)
SELECT
"row_id",
"in_member",
"in_invited",
"in_banned",
"status",
CASE WHEN "status" = 'ok' THEN (("in_member" OR "in_invited") AND (NOT "in_banned")) END AS "out_allow_entry"
FROM checked
ORDER BY "row_id";
SMT-LIB
; Tangibool SMT-LIB export (tangibool.smtlib/1) ; Profile: SMT-LIB 2.6 Boolean subset (QF_UF): Bool constants, define-fun, let, push/pop, assert, check-sat, echo. ; Tested with Z3 5.1.0 (z3-solver 5.2.0, WebAssembly build). ; Model: not stated ; Source revision: reference ; Interpretation status: not stated ; Exporter: 1.0.0 (engine 1.0.0; semantics tangibool-semantics/1) ; Logic digest: f0daa82174670c788f59eb058d07f7601cd0ace4ed94d61a747cc26c41fd4e0d ; Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78 ; Mode: decision ; ; Reading results: each query block states what sat and unsat mean for its question. A sat ; answer comes with a witness or counterexample (ask for it with (get-model) after sat only); ; unsat settles that scoped query and is solver-checked, not an independently checked proof ; certificate; unknown settles nothing. Blocks are scoped with push/pop, so assertions never ; accumulate across questions. This checks the supplied model, not whether it is a complete, ; legal, or safe statement of a real-world rule. ; ; Symbols (stable ID: name -> symbol): ; v_79df34978043: member -> in_member ; v_8afde06f51e3: invited -> in_invited ; v_60b2536f5dc8: banned -> in_banned ; f_ae8686d89791: allow_entry -> out_allow_entry (set-option :produce-models true) (set-info :smt-lib-version 2.6) (set-logic QF_UF) ; ---- Inputs (declared order) (declare-const in_member Bool) ; member (declare-const in_invited Bool) ; invited (declare-const in_banned Bool) ; banned ; ---- Outputs (dependencies first) ; output allow_entry (stable ID f_ae8686d89791): (member OR invited) AND NOT banned (define-fun out_allow_entry () Bool (and (or in_member in_invited) (not in_banned))) ; ---- Assumptions (the scope K; never folded into an output) ; K: conjunction of the enabled, confirmed assumptions (true when there are none) (define-fun K () Bool true) ; ---- Definitions only: nothing is asserted and no check is run. ; Add (assert ...) and (check-sat) inside (push 1) ... (pop 1) to ask a question.
LaTeX
allow_entry = \left(\mathit{member} + \mathit{invited}\right) \cdot \overline{\mathit{banned}}El error habitual
Escribir la regla de memoria como member OR invited AND NOT banned y confiar en que el lector la agrupe bien. La tabla de verdad muestra lo que hace la agrupación: la regla prevista es verdadera en tres filas, member OR (invited AND NOT banned) en cinco, y las dos filas de más tienen banned = VERDADERO.
Preguntas
¿Por qué la forma NOR necesita solo 2 compuertas y la forma NAND 11?
La regla es un OR que alimenta un AND con una entrada invertida, que es la forma natural de un NOR de un NOR: NOR(NOR(member, invited), banned). Las compuertas NAND tienen que construir el OR y la inversión con inversores, así que la construcción mecánica crece hasta 11.
¿Es (member AND NOT banned) OR (invited AND NOT banned) una forma mejor de la regla?
Es la misma función, igual en las ocho filas, y es la suma de productos que deriva el mapa de Karnaugh. Tiene un literal más que la original, así que ninguna de las dos es más corta en todos los sentidos; elige la que tus lectores entiendan antes.
Relacionado
Operadores y compuertas
- Compuerta NOT (inversor): tabla de verdad, símbolo y el operador NOT
- Compuerta AND (puerta Y): tabla de verdad de 2, 3 y 4 entradas, símbolo y expresión
- Compuerta OR (puerta O): tabla de verdad de 2, 3 y 4 entradas
Herramientas
- Generador de tablas de verdad: cualquier expresión booleana, hasta 12 variables, con columnas intermedias
- Calculadora y simplificador de álgebra de Boole paso a paso (cada ley nombrada y verificada)
- Solucionador de mapas de Karnaugh: de 2 a 4 variables, agrupaciones, SOP y POS
Véase también
- El error de la regla de entrada: socio OR (invitado AND NOT vetado) y el caso que difiere
- Precedencia de operadores en lógica booleana: NOT, luego AND, luego XOR, luego OR
- Generador de tablas de verdad: cualquier expresión booleana, hasta 12 variables, con columnas intermedias
- Reglas de elegibilidad: el patrón, las excepciones habituales y las pruebas
- Lección 4: Tablas de verdad
- Operadores booleanos en Python: and, or, not, precedencia y errores comunes
Ejemplos resueltos
Generado a partir del motor de Tangibool, semántica tangibool-semantics/1, motor 1.0.0, compilación . Cada tabla, mapa, simplificación y veredicto de estas páginas lo calculó el motor de Tangibool al compilar el sitio, y cada afirmación la volvió a comprobar el mismo verificador exacto que usa la app. Los límites se indican donde aplican. © 2026 Foreranger LTD.