- The combination of a formal language with a formal theory of truth or a proof theory (or both).
- The study of arguments, with the intention of describing how to distinguish good arguments from bad arguments. According to the generally accepted usage among philosophers, an argument is valid if (and only if) There are no cases in which the premises of the argument are true, but the conclusion of the argument false. A distinction is often made between valid arguments and cogent arguments. A cogent argument is a valid argument the premises of which are true. These terms only apply to what is called deductive logic, as opposed to inductive forms of reasoning.
- Some logics are classified as monotonic. Monotonic logics fit most closely what most people understand deductive logic to be. Roughly speaking, a logic is monotonic if (and only if) all deductively valid arguments formulated in that logic remain deductively valid, even if new premises are added to such arguments. Non-monotonic logics reflect what most people think of as inductive logic.
- Deductive reasoning is sometimes described as being most essentially inference from the general to the particular; inductive reasoning is sometimes described as being most essentially inference from the particular to the general. These descriptions are useful, but the two kinds of logic are best understood in terms of the degree of certainty conferred on the conclusion by the premises. Deductive arguments are those in which, in good arguments, the premises confer certainty on their conclusions. Deductive validity as described above embodies this requirement. Inductive arguments are those in which, in good arguments, the premises confer a degree of certainty less than total on their conclusions. In such arguments, the probability of the conclusion follows from the premises. # Other concepts and terms concerning logic, someone please add to this: propositional calculus (sentential logic), first-order logic, predicate logic, predicate calculus.