Concepts inReasoning about higher-order relational specifications

Recursive definition

In mathematical logic and computer science, a recursive definition (or inductive definition) is used to define an object in terms of itself . A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs. For example, the factorial function n! is defined by the rules 0! = 1. (n+1)! = (n+1)·n!. This definition is valid because, for all n, the recursion eventually reaches the base case of 0.  more from Wikipedia

Inductive reasoning

Inductive reasoning, also known as induction, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations of individual instances of members of the same class. Inductive reasoning contrasts with deductive reasoning in that a general conclusion is arrived at by specific examples.  more from Wikipedia

Formal system

A formal system is loosely speaking, any well defined system of abstract thought, on the model of mathematics. Technically, Euclid's elements, with a model consisting of 23 definitions and 10 postulates/axioms followed by 13 books of theorems with proof, is often held to be the first formal system and displays the characteristic of a formal system.  more from Wikipedia

Harrop formula

In intuitionistic logic, the Harrop formulae, named after Ronald Harrop, are the class of formulae inductively defined as follows: Atomic formulae are Harrop, including falsity (¿); is Harrop provided and are; is Harrop for any well-formed formula ; is Harrop provided is, and is any well-formed formula; is Harrop provided is.  more from Wikipedia

Definition

A definition (¿) is a passage that explains the meaning of a term, or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings. For each such specific sense, a definiens is a cluster of words that defines that term. A chief difficulty in managing definition is the need to use other terms that are already understood or whose definitions are easily obtainable. The use of the term in a simple example may suffice.  more from Wikipedia

First-order logic

First-order logic is a formal system used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less precise term). First-order logic is distinguished from propositional logic by its use of quantified variables.  more from Wikipedia

Logic

Logic (from the Greek ¿¿¿¿¿¿ logik¿) is the philosophical study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, ontology, epistemology, and ethics.  more from Wikipedia