# What is the term used for logic statements which are non reversible?

Something along the lines of If A then B, if B then not. A has to be true before B can be true but if B is true first then A isn't true. Is there a term describing this in logic or philosophy?

• I'm not entirely clear on what you're asking, but it sounds like you're describing the difference between sufficiency and necessity. Is that what you're looking for? Jun 23, 2015 at 2:59
• No Take-Backsies maybe? Jun 23, 2015 at 17:50
• @virmaior I was thinking along the lines of if A then B but not A if B Jun 23, 2015 at 21:23
• When you say "true first" do you mean temporally (which would make sense but require us to look at tensed logic) or logically (which would not make much sense)? Jun 24, 2015 at 14:49

## 3 Answers

The property you're looking for is called commutativity. We say a relation R is commutative if and only if aRb is logically equivalent to bRa. in a commutative relation order doesn't matter. In arithmetic addition is commutative because 2+3=3+2. In sentential Logic conjunction and disjunction and the biconditional are both commutative.

A relation is non-commutative if it isn't commutative. The material conditional is the only non-commutative binary relation in sentential logic. Division in arithmetic is noncommutative: 2/3 != 3/2

• Thank you this is the answer I was looking for, I guess I phrased the question poorly Mar 23, 2016 at 23:48

You have it switched, existence of a limit does not imply continuity (because it may not coincide with the value), but continuity does imply existence of a limit. Conditional statement with premise and conclusion switched is called the converse of the original. There is no special name either in mathematics or in logic for conditionals that are true without their converses, this is assumed by default, unless otherwise stated. On the contrary, conditionals that are true along with their converses are distinguished by terms "biconditional" or "logical equivalence". "Irreversible" or "non-reversible" may be used informally, but they are not terms.

• Thaaaaamk you, and yes I was trying to use a math which would make sense but I messed up the wording. Jun 22, 2015 at 3:35

As Conifold pointed out, there is no specific name for conditionals that are true without their converses in logic proper. However, in the theory of computation, there is a "reversible logic", where the term logic is used in the sense of logic gates.
The key consideration is that the relationship between the inputs and the outputs has to be injective (i.e. a one to one mapping), for this to be possible.