# Logic Equation Definition

### Declaration Sentences

*LOGIC EQUATION* is a reserved word to specify a logic proposition, name must be provided by the user, it must follow the rules of any constraint name.

The generic sintaxis is: LOGIC EQUATION name

**Examples:**
Some examples could be like the following ones:

LOGIC EQUATION ATMOST1, ATMOST2, ATMOST3, IMP0, IMP1, IMP2;

### Definition Sentence

Logic propositions are used to pose relationships between the Boolean (Binary) variables handling the disjunctive terms. Logic Propositions must be declared and defined in the GAMS Section. The definition of a LOGIC EQUATION is similar to any other equation in the GAMS model *(see Chapter 8. Equations in the GAMS Users Guide)*, with the difference that is must include only the following operators:

Operator Symbol |
Operation |

**->** |
Implication |

**<->** |
equivalence |

**not** |
negation |

**and** |
logical and |

**or** |
logical or |

**xor** |
exclusive or |

**Examples:**
Some definition sentences could be like the following ones:

ATMOST1.. Y('1') xor Y('2');

ATMOST2.. Y('4') xor Y('5');

ATMOST3.. Y('6') xor Y('7');

IMP0.. Y('1') -> Y('3') or Y('4') or Y('5');

IMP1.. Y('2') -> Y('3') or Y('4') or Y('5');

IMP2.. Y('3') -> Y('8')