Above art by Steve McCaffery

This is just meant to be a surmise of formal #logic, via tables of #operators or #quantifiers, rules of #computation, and a glossary of relevant terms.

Logic

Logic is the study of the “correct” way by which some alleged verbally expressed derivation from verbally expressed past knowledge, without reliance on mere intuition or perception, can be determined to constitute new knowledge. Reiterated, it is the study of the “correct” way to derive new verbally expressed knowledge from established verbally-expressed knowledge without reliance on mere intuition or perception.

Truth-Values and Evidence

For logic, a truth-value is an epistemically relevant value that is assigned to a sentence. The epistemic relevance of such a value is that it distinguishes and distributes the status a sentence may have for knowledge, called its epistemic status. A proposition is a verbal expression that can have or take a truth-value. Systems of logic that only have $2$ truth-values with opposite valences, namely true v. false, are characterized as following the principle of bivalence and may thus be called a bivalent logic. The paradigmatic proposition is a meaningful declarative sentence.

Relationships among or within propositions that are alleged to possess specific truth-values that allow or determine a truth-value to be granted for some other proposition or set of propositions are said to be evidential in relation to that or those other proposition(s), hence constituting an evidential relationship. When a #proposition is claimed or alleged to have a specific truth-value, namely one which would warrant it a favorable epistemic status, it is called an assertion. A set of propositions with an asserted evidential relationship among themselves is known as an argument, whereby the subset of propositions acting as evidence are known as premises and the propositions evidenced by them are known as conclusions. The process of going from a #premise to a #conclusion in an #argument is known as an inference.

Formal Logic

Formal logic is logic which focuses on studying evidential relationships among or within sentences independent of what those sentences are about or regarding, what utility they serve, or what they refer to. The latter may be called the content of the sentence. Without the content, what is left of a sentence is its form, i.e. the relationships among its components—that is, the structure of the sentence. Types of formal logic include propositional calculus, predicate calculus, etc.

Validity

Validity refers to a property of a formal aspect of an evidential relationship such that the form of that relationship is truth-preserving. Truth preservation is the process by which the (intrinsically?) epistemically favored truth-value, or “positively valent” truth-value, found in the premises of the argument, or the components of the premises of the argument, persist in the conclusion(s) and/or is “transferred” to the conclusion(s) itself/themselves as a whole. Namely, under a principle of bivalence, if the premises of an argument being true guarantee the truth of its conclusion, or the conclusion of an argument cannot be false provided its premises are true, then that argument can be described as valid. Otherwise, the argument would be described as invalid. An argument which is valid while in fact the premises are also true is described as sound. For testing if an argument is valid or invalid, skip to Validity Testing.

Informal Logic

Informal logic is logic which assesses the derivation of verbally-expressed knowledge in terms of the context that determines the scope of those verbal expressions, in addition to the forms which determine them, such that they can be regarded as knowledge. Unsurprisingly, informal logic renders the content of the sentence, i.e. its utility, reference, or object, relevant, as it has baring on questions of scope.