Font Size:

Set-Oriented Logical Connectives: Syntax and Semantics

Last modified: 2010-04-27

#### Abstract

Of the common commutative binary logical connectives, only

`and`

and `or`

may be used as operators that take arbitrary numbers of arguments with order and multiplicity being irrelevant, that is, as connectives that take sets of arguments. This is especially evident in the Common Logic Interchange Format, in which it is easy for operators to be given arbitrary numbers of arguments. The reason is that `and`

and `or`

are associative and idempotent, as well as commutative. We extend the ability of taking sets of arguments to the other common commutative connectives by defining generalized versions of `nand`

, `nor`

, `xor`

,and `iff`

, as well as the additional, parameterized connectives `andor`

and `thresh`

. We prove that `andor`

is expressively complete — all the other connectives may be considered abbreviations of it.#### Keywords

Knowledge Representation; Reasoning; Logic; Common Logic Interchange Format; CLIF

Full Text:
PDF