Elements of Logic

The elements of logic are the fundamental building blocks of logical theories that describe the logical conceptualization of some system that is natural or designed (a.k.a. man-made). A logical system is a type of designed system.  The elements of logic can also describe knowledge within some area of knowledge using these building blocks.

Here is a list of those building blocks, the elements of logic:

  • Logical statement: A logical statement is a proposition, claim, assertion, belief, idea, or fact about or related to the area of knowledge to which the logical conceptualization relates.  A logical statement is a declarative sentence.  Not all sentences are statements; for example, a question such as "What is your name?", or a command such as "Stop!", are not statements.  There are five broad categories of logical statements: (these can be thought of as logical molecules)
      • Terms: Terms are important logical statements that define ideas or "things" used by a logical conceptualization.  For example, “assets”, “liabilities”, “equity”, and “balance sheet” are things or ideas used in a logical conceptualization to describe the area of knowledge referred to as financial reporting.
      • Associations: Associations are important logical statements that describe permissible interrelationships between the terms such as “assets is part-of the balance sheet” or “operating expenses is a type-of expense” or “an asset is a ‘debit’ and is ‘as of’ a specific point in time and is always a monetary numeric value”. Associations can be grouped into two broad types:
        • "Is-a" (a.k.a. general-special, association, type-subtype, class-subclass, equivalent-class)
        • "Has-a" (a.k.a. part-of, has-part, part-whole, composition, aggregation)
      • Rules: Rules (a.k.a. assertions, restrictions, constraints) are important logical statements that describe what tend to be convertible into IF…THEN…ELSE types of relationships such as “IF the economic entity is a not-for-profit THEN net assets = assets - liabilities; ELSE assets = liabilities + equity”.  One rule can be connected to another rule using logic gates (a.k.a. logical connective) (AND, OR, NOR, NAND, XOR, XNOR, NOT) to form complex logical statements. Rules can assert mathematical relationships or derive mathematical relationships to form new facts.
      • Facts: Facts are important logical statements that are held out as being true. In the context of databases and knowledge representation, facts are often used to represent known information. For example, facts are logical statements about the numbers and words that are provided by an economic entity within a financial report.  For example, the financial report might state “assets for the consolidated legal entity Microsoft as of June 20, 2017 was $241,086,000,000 expressed in US dollars and rounded to the nearest millions of dollars.
      • Properties: Properties are important logical statements about the important qualities and traits of a model, structure, term, association, rule, and fact.
  • Axioms: Axioms are foundational logical statements that are fundamentally accepted as being true per some logical system.
  • Theorems: Theorems are logical statements that are determined to be true per logical steps that can be taken to arrive at a conclusion using axioms, other theorems, or facts.
  • Restriction: Restrictions are a special type of axiom or theorem that is imposed by some authority which chooses to restrict, constrain, limit, or otherwise impose some range on some logical artifact.
  • Classification: Classification is the grouping of logical artifacts into sets. (a.k.a. types)
  • Logical structure: A logical structure is as set of logical statements which describe the structure (a.k.a. assembly). An "infon" which is defined by Situation Theory is a unit of information. In infon is a type of logical structure.  An infon is a useful, convenient unit or "set" of information.
  • Logical model: A logical model is a set of specific structures that are consistent with and permissible interpretations of that model.  Models add flexibility to logical conceptualizations.
  • Logical conceptualization: A logical conceptualization is a set of models that are consistent with and permissible per that logical conceptualization. A logical conceptualization is made up of a set of models, structures, terms, associations, rules, and facts.
  • Logical theory: A logical theory is described per some logical conceptualization that forms a logical theory that explains what is permitted and what is not permitted per a logical conceptualization which is made up of a set of logical models, structures, terms, associations, rules, and facts.
  • Logical system: A logical system can be explained by a logical theory.  A logical theory is an abstract conceptualization of specific important details of some area of knowledge. The logical theory provides a way of thinking about an area of knowledge by means of deductive reasoning to derive logical consequences of the logical theory.
  • Archetype: An archetype is a typical example of something, a template. An archetype can be seen as a good practices pattern; canonical form.

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