I don't know why people take offense to word argument and spoil relationships....see meaning at dictionary.com and wikipedia.org

http://dictionary.reference.com/browse/argument

ar·gu·ment  

1.

an oral disagreement; verbal opposition; contention;

2.

a discussion involving differing points of view; debate: They were deeply involved in an argument about inflation.

3.

a process of reasoning; series of reasons: I couldn't follow his argument.

—Synonyms
1. Argument, controversy, dispute  imply the expression of opinions for and against some idea. An argument  usually arises from a disagreement between two persons, each of whom advances facts supporting his or her own point of view. A controversy  or a dispute  may involve two or more persons. A dispute  is an oral contention, usually brief, and often of a heated, angry, or undignified character: a violent dispute over a purchase.  A controversy  is an oral or written expression of contrary opinions, and may be dignified and of some duration: a political controversy.

Legal Dictionary

Main Entry: ar·gu·ment
Function: noun
1 :  a reason or the reasoning given for or against a matter under discussion —compare EVIDENCE, PROOF
2 :  the act or process of arguing, reasoning, or discussing;

Argument

From Wikipedia, the free encyclopedia

This article is about the word as it is used in logic. For other uses, see Argument (disambiguation).

An argument in logic is a set of one or more meaningful declarative sentences (or "propositions") known as the premises along with another sentence known as the conclusion. Some authors refer to the premises and conclusion using the terms declarative sentence, statement, proposition, sentence, or even indicative utterance. The reason for the variety is concern about the ontological significance of the terms, proposition in particular.

There are several kinds of arguments, the best-known of which are "deductive" and "inductive." A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises. An inductive argument, on the other hand, asserts that the truth of the conclusion is supported by the premises. Each premise and the conclusion are truth bearers or "truth-candidates", capable of being either true or false (and not both). While statements in an argument are referred to as being either true or false, arguments are referred to as being valid or invalid (see logical truth). A deductive argument is valid if and only if the truth of the conclusion is entailed by (is a logical consequence) of the premises, and its corresponding conditional is therefore a logical truth. A sound argument is a valid argument with true premises; a valid argument may well have false premises.