## 23 terms

### quantificationally true

A sentence P of PL is quantificationally true if and only if P is true on every interpretation

### quantificationally false

A sentence P of PL is quantificationally false if and only if P is false on every interpretation

### quantificationally indeterminate

A sentence P if PL is quantificationally indeterminate if and only if P is neither quantificationally true nor quantificationally false

### quantificationally equivalent

Sentences P and Q of are quantificationally equivalent if and only if there is no interpretation on which P and Q have different truth values

### quantificationally consistent

A set of sentences of PL is quantificationally consistent if and only if there is at least one interpretation on which all the members of the set are true

### quantificationally valid

An argument of PL is quantificationally valid if and only if there is no interpretation on which every premise is true and the conclusion is false

### function

an operation that takes one or more elements of a set as arguments and returns a single value

### A predicate is...

a function that takes one or more objects as the values of its variable and returns a truth-value

### A functor is...

a function that takes one or more objects as the values of its variables and returns an object

### quantificationally entails

a set gamma of sentences of PL quantificationally entails a sentence P of PL if and only if there is no interpretation on which all the members of the set are true and P is false

### Sentence of PL

A formula of PL is a sentence of PL if and only if no occurrence of a variable is P is free

### Open Sentence of PL

A formula of PL is an open sentence of PL if and only if there is at least one occurrence of a variable in P that is free

### Bound Variable

An occurrence of a variable x in a formula P of PL that is within the scope of the x-quantifier

### Scope of a quantifier of PL

The scope of a quantifier in a formula P of PL is the subformula Q of P of which that quantifier is the main logical operator

### Atomic Formulas of PL

Every expression of PL that is either a sentence letter of PL or an n-place predicate of PL followed by n individual terms of PL

### An interpretation assigns...

a universe of discourse, truth-values to the sentence letters of PL, elements of the universe of discourse to the constants of PL, a set of ordered n-tuples