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Regla de alarma: armada AND (puerta OR ventana OR movimiento) AND NOT codigo

Una regla de alarma, armed AND (door OR window OR motion) AND NOT disarm_code: una tabla de 32 filas con siete que disparan, una FND de tres términos, 14 compuertas NOR frente a 47 NAND, y sin mapa con cinco variables.

La alarma suena cuando el sistema está armado, algún sensor salta y no se ha introducido un código de desarme válido. La lectura del motor enumera los tres requisitos: armed verdadero, al menos uno entre door, window y motion, y disarm_code falso. Cinco entradas dan una tabla de 32 filas, y la salida es verdadera en siete, Σm(18, 20, 22, 24, 26, 28, 30): cada combinación no vacía de los tres sensores, con el sistema armado y sin código introducido.

Las comprobaciones: no es tautología, contraejemplo las cinco entradas en FALSO; satisfacible, testigo armed = VERDADERO, door = FALSO, window = FALSO, motion = VERDADERO, disarm_code = FALSO. El simplificador no encontró ninguna ley que acorte la regla de cinco operadores, y la FNC es la original, tres cláusulas. El conversor a FND aplica dos distributividades y da tres términos de tres literales, uno por sensor, como (armed AND door AND NOT disarm_code). Compuertas: 47 NAND y 14 NOR. El mapa de Karnaugh no está disponible con cinco variables; el mapa del motor cubre hasta cuatro.

La lógica de una alarma es una regla de seguridad, así que las dos condiciones negativas merecen atención: el sistema no debe sonar desarmado, y no debe quedarse callado armado y con un sensor saltado. Las 25 filas falsas cubren lo primero, las siete verdaderas lo segundo. Vigila disarm_code, que prevalece sobre todos los sensores; en la fórmula va unido con AND en el nivel superior, y una versión que lo metiera dentro del OR de sensores dejaría que una puerta abierta prevaleciera sobre el código. Para una función de este tamaño, la tabla y las comprobaciones exactas, no un mapa, son las herramientas.

alarm := armed AND (door OR window OR motion) AND NOT disarm_code · salida

Comprobaciones exactas

¿Siempre verdadera (tautología)? No Contraejemplo: armed = F, door = F, window = F, motion = F, disarm_code = F · Exhaustively checked and solver cross-checked · 1 filas
¿Siempre falsa (contradicción)? No Contraejemplo: armed = V, door = F, window = F, motion = V, disarm_code = F · Exhaustively checked and solver cross-checked · 19 filas
¿Puede ser verdadera? Sí Asignación de ejemplo: armed = V, door = F, window = F, motion = V, disarm_code = F · Exhaustively checked and solver cross-checked · 19 filas

Tabla de verdad (32 filas)

Regla de alarma: armada AND (puerta OR ventana OR movimiento) AND NOT codigo
#armeddoorwindowmotiondisarm_codealarm
0FALSOFALSOFALSOFALSOFALSOFALSO
1FALSOFALSOFALSOFALSOVERDADEROFALSO
2FALSOFALSOFALSOVERDADEROFALSOFALSO
3FALSOFALSOFALSOVERDADEROVERDADEROFALSO
4FALSOFALSOVERDADEROFALSOFALSOFALSO
5FALSOFALSOVERDADEROFALSOVERDADEROFALSO
6FALSOFALSOVERDADEROVERDADEROFALSOFALSO
7FALSOFALSOVERDADEROVERDADEROVERDADEROFALSO
8FALSOVERDADEROFALSOFALSOFALSOFALSO
9FALSOVERDADEROFALSOFALSOVERDADEROFALSO
10FALSOVERDADEROFALSOVERDADEROFALSOFALSO
11FALSOVERDADEROFALSOVERDADEROVERDADEROFALSO
12FALSOVERDADEROVERDADEROFALSOFALSOFALSO
13FALSOVERDADEROVERDADEROFALSOVERDADEROFALSO
14FALSOVERDADEROVERDADEROVERDADEROFALSOFALSO
15FALSOVERDADEROVERDADEROVERDADEROVERDADEROFALSO
16VERDADEROFALSOFALSOFALSOFALSOFALSO
17VERDADEROFALSOFALSOFALSOVERDADEROFALSO
18VERDADEROFALSOFALSOVERDADEROFALSOVERDADERO
19VERDADEROFALSOFALSOVERDADEROVERDADEROFALSO
20VERDADEROFALSOVERDADEROFALSOFALSOVERDADERO
21VERDADEROFALSOVERDADEROFALSOVERDADEROFALSO
22VERDADEROFALSOVERDADEROVERDADEROFALSOVERDADERO
23VERDADEROFALSOVERDADEROVERDADEROVERDADEROFALSO
24VERDADEROVERDADEROFALSOFALSOFALSOVERDADERO
25VERDADEROVERDADEROFALSOFALSOVERDADEROFALSO
26VERDADEROVERDADEROFALSOVERDADEROFALSOVERDADERO
27VERDADEROVERDADEROFALSOVERDADEROVERDADEROFALSO
28VERDADEROVERDADEROVERDADEROFALSOFALSOVERDADERO
29VERDADEROVERDADEROVERDADEROFALSOVERDADEROFALSO
30VERDADEROVERDADEROVERDADEROVERDADEROFALSOVERDADERO
31VERDADEROVERDADEROVERDADEROVERDADEROVERDADEROFALSO

Lectura en lenguaje claro

Principiantealarm es verdadero exactamente cuando se cumplen todas las condiciones siguientes:
1. armed es verdadero
2. al menos uno entre door, window y motion es verdadero (pueden serlo varios)
3. disarm_code es falso
En todos los demás casos, alarm 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.
Intermedioalarm es verdadero exactamente cuando se cumplen todas las condiciones siguientes:
1. armed es verdadero
2. al menos uno entre door, window y motion es verdadero (pueden serlo varios)
3. disarm_code es falso
En todos los demás casos, alarm es falso.
Avanzadoalarm es verdadero exactamente cuando se cumplen todas las condiciones siguientes [conjunción ∧]:
1. armed es verdadero
2. al menos uno entre door, window y motion es verdadero (pueden serlo varios) [disyunción inclusiva ∨]
3. disarm_code es falso [negación ¬]
En todos los demás casos, alarm es falso.
Notación formal: armed ∧ (door ∨ window ∨ motion) ∧ ¬disarm_code

Diagrama lógico

Alarm rule: armed AND (door OR window OR motion) AND NOT disarm_code Alarm rule: armed AND (door OR window OR motion) AND NOT disarm_code armed door window motion disarm_code alarm AND OR NOT
Alarm rule: armed AND (door OR window OR motion) AND NOT disarm_code Alarm rule: armed AND (door OR window OR motion) AND NOT disarm_code armed door window motion disarm_code alarm AND OR NOT

Simplificación paso a paso

El motor no encontró ninguna ley que acorte esta expresión; ya es tan corta como sus leyes de reescritura permiten.

armed AND (door OR window OR motion) AND NOT disarm_code

Mapa de Karnaugh

Un mapa de Karnaugh muestra como máximo 4 variables; esta expresión tiene más. Usa la herramienta para fijar algunas entradas y ver un corte etiquetado. alarm depends on 5 inputs that are not shown to be irrelevant; a Karnaugh map shows at most 4. Fix disarm_code to view an explicitly labelled slice.

Mintérminos y maxtérminos

alarm(armed, door, window, motion, disarm_code) = Σm(18, 20, 22, 24, 26, 28, 30)alarm(armed, door, window, motion, disarm_code) = ΠM(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31)

Orden de variables: armed, door, window, motion, disarm_code · 32 filas

Formas normales

Forma normal conjuntiva (FNC)

armed AND (door OR window OR motion) AND NOT disarm_code

3 cláusulas, 5 literales · complete

Forma normal disyuntiva (FND)

(armed AND door AND NOT disarm_code) OR (armed AND window AND NOT disarm_code) OR (armed AND motion AND NOT disarm_code)

3 términos, 9 literales · complete · Distributividad ×2

Solo NAND, solo NOR

Forma solo con NAND

NAND(NAND(NAND(NAND(armed, NAND(NAND(NAND(NAND(door, door), NAND(window, window)), NAND(NAND(door, door), NAND(window, window))), NAND(motion, motion))), NAND(armed, NAND(NAND(NAND(NAND(door, door), NAND(window, window)), NAND(NAND(door, door), NAND(window, window))), NAND(motion, motion)))), NAND(disarm_code, disarm_code)), NAND(NAND(NAND(armed, NAND(NAND(NAND(NAND(door, door), NAND(window, window)), NAND(NAND(door, door), NAND(window, window))), NAND(motion, motion))), NAND(armed, NAND(NAND(NAND(NAND(door, door), NAND(window, window)), NAND(NAND(door, door), NAND(window, window))), NAND(motion, motion)))), NAND(disarm_code, disarm_code)))

47 compuertas · equivalencia verificada en todas las filas

Forma solo con NOR

NOR(NOR(NOR(NOR(armed, armed), NOR(NOR(NOR(door, window), NOR(door, window)), motion)), NOR(NOR(armed, armed), NOR(NOR(NOR(door, window), NOR(door, window)), motion))), disarm_code)

14 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: 500e0e0a87d4b3c8e00645a893e9d0928876e6a9aca62ea11163e1787c2e2dc7
Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78

Inputs (dict keys, declared order) and generated parameter names:
    'armed' -> input_armed
    'door' -> input_door
    'window' -> input_window
    'motion' -> input_motion
    'disarm_code' -> input_disarm_code

Outputs (declared order) and their functions:
    'alarm' -> output_alarm(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({'armed': False, 'door': False, 'window': False, 'motion': False, 'disarm_code': False})
    # -> {'alarm': False}
    model.output_alarm({'armed': False, 'door': False, 'window': False, 'motion': False, 'disarm_code': False})
    # -> False
    model.evaluate({'armed': 1, 'door': False, 'window': False, 'motion': False, 'disarm_code': 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_alarm",
]

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": "500e0e0a87d4b3c8e00645a893e9d0928876e6a9aca62ea11163e1787c2e2dc7",
    "assumptions_digest": "d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78",
    "primary_output": "alarm",
    "unused_inputs": (),
    "subcircuits": (),
}

# Stable ID -> generated identifier (reversible mapping; names are exact, escaped strings).
IDENTIFIER_MAP = {
    "v_edcc9b841713": {"kind": "input", "name": "armed", "identifier": "input_armed"},
    "v_4be2c65e6435": {"kind": "input", "name": "door", "identifier": "input_door"},
    "v_8032c9854781": {"kind": "input", "name": "window", "identifier": "input_window"},
    "v_79fcbe2fca27": {"kind": "input", "name": "motion", "identifier": "input_motion"},
    "v_262f657322b9": {"kind": "input", "name": "disarm_code", "identifier": "input_disarm_code"},
    "f_b136ce8a03d7": {"kind": "output", "name": "alarm", "identifier": "output_alarm"},
}

INPUT_NAMES = ("armed", "door", "window", "motion", "disarm_code")
OUTPUT_NAMES = ("alarm",)
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_alarm(input_armed: bool, input_door: bool, input_window: bool, input_motion: bool, input_disarm_code: bool) -> bool:
    """Decision output 'alarm': armed AND (door OR window OR motion) AND NOT disarm_code"""
    return input_armed and (input_door or input_window or input_motion) and (not input_disarm_code)


# ---- Public API ----


def output_alarm(inputs: Mapping[str, bool], *, check_scope: bool = True) -> bool:
    """Decision output 'alarm' (stable ID f_b136ce8a03d7).

    'alarm' := armed AND (door OR window OR motion) AND NOT disarm_code

    Required inputs: 'armed', 'door', 'window', 'motion', 'disarm_code'.
    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, ("armed", "door", "window", "motion", "disarm_code"), check_scope)
    if check_scope:
        _require_in_scope(values)
    output_alarm_value = _compute_output_alarm(values["armed"], values["door"], values["window"], values["motion"], values["disarm_code"])
    return output_alarm_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: 'armed', 'door', 'window', 'motion', 'disarm_code'.
    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, ("armed", "door", "window", "motion", "disarm_code"), check_scope)
    if check_scope:
        _require_in_scope(values)
    output_alarm_value = _compute_output_alarm(values["armed"], values["door"], values["window"], values["motion"], values["disarm_code"])
    return {
        "alarm": output_alarm_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: 500e0e0a87d4b3c8e00645a893e9d0928876e6a9aca62ea11163e1787c2e2dc7
-- 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_edcc9b841713: armed -> "in_armed"
--   v_4be2c65e6435: door -> "in_door"
--   v_8032c9854781: window -> "in_window"
--   v_79fcbe2fca27: motion -> "in_motion"
--   v_262f657322b9: disarm_code -> "in_disarm_code"
-- Output columns:
--   f_b136ce8a03d7: alarm -> "out_alarm"
-- 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_alarm] output alarm (stable ID f_b136ce8a03d7)
--   alarm := armed AND (door OR window OR motion) AND NOT disarm_code
--   PRECONDITION: "in_armed", "in_door", "in_window", "in_motion", "in_disarm_code" are non-NULL booleans.
--   ("in_armed" AND ("in_door" OR "in_window" OR "in_motion") AND (NOT "in_disarm_code"))
--

-- ----------------------------------------------------------------------------------------------
-- 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_armed", "in_door", "in_window", "in_motion", "in_disarm_code") AS (
  -- tangibool:example-rows:begin
  VALUES
    (1, FALSE, FALSE, FALSE, FALSE, FALSE),
    (2, TRUE, TRUE, TRUE, TRUE, TRUE),
    (3, NULL::boolean, FALSE, FALSE, FALSE, FALSE)
  -- tangibool:example-rows:end
),
checked AS (
  SELECT
    inputs.*,
    CASE
      WHEN "in_armed" IS NULL OR "in_door" IS NULL OR "in_window" IS NULL OR "in_motion" IS NULL OR "in_disarm_code" IS NULL THEN 'invalid_input'
      ELSE 'ok'
    END AS "status"
  FROM inputs
)
SELECT
  "row_id",
  "in_armed",
  "in_door",
  "in_window",
  "in_motion",
  "in_disarm_code",
  "status",
  CASE WHEN "status" = 'ok' THEN ("in_armed" AND ("in_door" OR "in_window" OR "in_motion") AND (NOT "in_disarm_code")) END AS "out_alarm"
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: 500e0e0a87d4b3c8e00645a893e9d0928876e6a9aca62ea11163e1787c2e2dc7
; 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_edcc9b841713: armed -> in_armed
;   v_4be2c65e6435: door -> in_door
;   v_8032c9854781: window -> in_window
;   v_79fcbe2fca27: motion -> in_motion
;   v_262f657322b9: disarm_code -> in_disarm_code
;   f_b136ce8a03d7: alarm -> out_alarm

(set-option :produce-models true)
(set-info :smt-lib-version 2.6)
(set-logic QF_UF)

; ---- Inputs (declared order)
(declare-const in_armed Bool) ; armed
(declare-const in_door Bool) ; door
(declare-const in_window Bool) ; window
(declare-const in_motion Bool) ; motion
(declare-const in_disarm_code Bool) ; disarm_code

; ---- Outputs (dependencies first)
; output alarm (stable ID f_b136ce8a03d7): armed AND (door OR window OR motion) AND NOT disarm_code
(define-fun out_alarm () Bool (and in_armed (or in_door in_window in_motion) (not in_disarm_code)))

; ---- 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
alarm = \mathit{armed} \cdot \left(\mathit{door} + \mathit{window} + \mathit{motion}\right) \cdot \overline{\mathit{disarm\_code}}

El error habitual

Escribir los sensores con AND, door AND window AND motion, de modo que la alarma necesite que salten todos a la vez. La regla prevista es verdadera en siete filas; la versión con AND, en una. La lista de mintérminos, con sus siete entradas, muestra que cualquier sensor por sí solo debe bastar.

Preguntas

¿Por qué los siete mintérminos son números pares entre 18 y 30?

armed es el bit más significativo, que aporta 16, y disarm_code es el menos significativo, que debe ser 0, así que toda fila que dispara es par y al menos 16. Los tres bits de sensor suman 2, 4 u 8 en cualquier combinación no vacía, dando los siete valores de 18 a 30.

Relacionado

Operadores y compuertas

Herramientas

Véase también

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.