1

I've learned how to do truth tables with the different syntaxes (conjunction, disjunction, etc.), but when it comes to 3-5 atomic sentences it takes too long to do a full truth table with 8-32 lines. Is there another way to come to a conclusion if the sentence is valid or invalid?

This is not exactly a dupe, but see http://philosophy.stackexchange.com/questions/30139/how-do-i-check-if-two-logical-expressions-are-equivalent/30141#30141

– virmaior – 2016-09-28T04:07:13.0131

Also relevant http://philosophy.stackexchange.com/questions/17643/invalid-arguments-with-true-premises-and-true-conclusion/17648#17648 . There's two ways to do truth-tables (full table and short circuit).

– virmaior – 2016-09-28T04:08:04.027@virmaior thanks! Short circuit was exactly what I needed. – K.Wong – 2016-09-28T04:26:20.450

Short circuit is the more specific case of https://en.wikipedia.org/wiki/Unification_(computer_science) -- you just apply simplification rules over and over again until you have a truth value, as if you were evaluating an arithmetic equality, or doing algebra.

– None – 2016-09-28T18:02:37.920take a look at tableaux: https://en.m.wikipedia.org/wiki/Method_of_analytic_tableaux Smullyan's First Order Logic is a (cheap!) small masterpiece that shows how to use them.

– None – 2016-09-28T19:31:34.077