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What (who) is logic variables - definition

SYSTEMATIC LOGICAL PROCESS CAPABLE OF DERIVING A CONCLUSION FROM HYPOTHESES

Laws of Logic; Inference rule; Rules of inference; Rules of derivation; Inference rules; Universal Variables; Law of logic; Transformation rules; Transformation rule (logic); Transformation rule; Rules of logic

free variable

$Tree summarizing the syntax of the expression <math>\forall x\, ((\exists y\, A(x)) \vee B(z)) </math>$

CLASSIFICATION OF VARIABLES IN A LOGIC FORMULA BASED ON WHETHER OR NOT THEY ARE INSIDE THE SCOPE OF A QUANTIFIER

Free variable; Bound variable; Variable binding operation; Variable-binding operation; Free variables; Bound variables; Unbound variable; Unbound variables; Variable-binding operator; Variable binding operator; Free and bound variables; Bound variable clash; Free and bound variable; Placeholder (computer programming); Free variables & bound variables; Free occurrence; Placeholder variable; Apparent variable

1. A variable referred to in a function, which is not an argument of the function. In lambda-calculus, x is a {bound variable} in the term M = x . T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm x . U then x is rebound in this term. This nested, inner binding of x is said to "shadow" the outer binding. Occurrences of x in U are free occurrences of the new x. Variables bound at the top level of a program are technically free variables within the terms to which they are bound but are often treated specially because they can be compiled as fixed addresses. Similarly, an identifier bound to a recursive function is also technically a free variable within its own body but is treated specially. A closed term is one containing no free variables. See also closure, lambda lifting, scope. 2. In logic, a variable which is not quantified (see quantifier).

Two-variable logic

Two-variable logic with counting; Two-variable fragment

In mathematical logic and computer science, two-variable logic is the fragment of first-order logic where formulae can be written using only two different variables.L.

https://en.wikipedia.org/wiki/Two-variable_logic

Mathematical logic

SUBFIELD OF MATHEMATICS

Symbolic Logic; Symbolic logic; Mathematical Logic; Logic (mathematics); Logic (math); Logic (maths); Logic (symbolic); Mathematical logician; Logic modeling; Logic modelling; Formal Logic; History of mathematical logic; Subfields of mathematical logic; Formal logical systems; History of symbolic logic; Applications of mathematical logic; 20th century in mathematical logic

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory.

https://en.wikipedia.org/wiki/Mathematical_logic

Wikipedia

Rule of inference

In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion.

Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a given set of formulae according to the rule. An example of a rule that is not effective in this sense is the infinitary ω-rule.

Popular rules of inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical quantifiers.

https://en.wikipedia.org/wiki/Rule of inference