Logic Systems

The semantics of first-order logic are agreed to and very well understood.  However, not everyone uses the same terminology to describe their understanding of first-order logic so there tend to be many different descriptions of first-order logic using different terminology.  There is no one agreed upon standard description of first order logic.  Current descriptions of first-order logic tend to be technical in nature.  None of those versions are both complete and explained in terms that a business professional can understand.  For example, current descriptions seem to enable the description of the necessary "privative" artifacts and imply the notion of higher level artifacts, but don't explicitly provide common higher level artifacts.  (An example of defining higher level artifacts is provided by Atomic Design Methodology.)

And, therefore, I have to come up with my own set of terminology and description to describe what I am trying to describe in terms that are approachable by business professionals.  I will provide my version of a complete description which is approachable by liberal arts majors now:

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Logic is a formal set of principles and rules that form a framework for correct reasoning and communications.  There are many different logics and there are many different technical approaches to implementing of logics.  (To keep this simple I am simply going to tell you that the logic that I am using which is a safely implementable subset of first-order logic called Horn Logic or DATALOG that is safe to use and also very powerful when implementing computability.)

A system is a formal group of interacting or interrelated parts that act according to a set of known and understood logic rules to form a unified whole to achieve some specific known and understood set of goals/objectives for some specific known set of stakeholders.  A system is a set of parts (a.k.a. elements, things, atoms) that work together and that form a whole.  A system has known and understood boundaries.  A system can be natural, such as the solar system, or designed by humans, such as a bicycle. A system tends to have some deliberate, intentional aim; it has goal(s) and/or objective(s). A designed system tends to be describable. My focus here is explicitly defined designed systems specified by humans. (a.k.a. formal system)

A logic statement is a proposition, claim, assertion, axiom, belief, idea, fact, or truth about or related to a logic system.  A logic statement is a piece of information.  A logic statement is declarative (e.g. not a question). A logic statement is a formal statement of truth about the workings of some detail of some specific logic system.  A logic statement at the same time describes/specifies a system, can be used to construct/create per that system, verify that the system is working per the description/specification, extract/analyze or otherwise work with system information.

A logic system (a.k.a. formal system ) is a group of interacting or interrelated logic statements that act according to a set of logic patterns to form a unified whole or conceptualization.  A logic system is the set of logic statements that defines that logic system.  A set of logic statements forms a logic theory that explains the dynamics of the logic system.

A logic theory is a logic system that provides a formal, explicit, deliberate specification of the important specific details of an intended shared conceptualization between a set of stakeholders of a logic system for an area of knowledge to achieve some specific set of goals/objectives.  The logic theory describes the aim of the logic system.  A logic theory forms a conceptualization.

• Conceptualization: Set of declarative logic statements that describe what is permissible per a system. Conceptualizations describe/specify, enable creation/construction, enable review/verification, and enable extraction/analysis.
• Model: Set of logic statements that form/describe structures that are consistent with and permissible interpretations of that model. Models provide system flexibility.
• Term: Logic statement that defines/describes an idea/thing which is used within the logical conceptualization and distinguishes one idea/thing from other ideas/things. Ideas/things tend to be nouns. (a.k.a. thing, concept, entity, class, idea)
• Structure: Set of logic statements and type of term which describe assemblies of terms, associations, and restrictions.  A structure is an assembly of terms, associations, restrictions that are consistent with and permissible per that structure (compound, decomposable). A structure is a compound idea/thing and can be decomposed. Structures provide the ability to identify, refer to, and work with sets of ideas/things.
• Association: Logic statement that describes a permissible interrelationship between an idea/thing within a structure. Associations tend to be verbs. (a.k.a. relation, hierarchy)
• Categorization (is-a): Logic statement and type of association that formally groups or classifies an idea/thing into a useful set. A type is an important category of association. (a.k.a. class, subclass, superclass, generalization, specialization, wider, narrower)
• Compositional (has-a): Logic statement and type of association that indicates that an idea/thing is part of some other idea/thing (a.k.a. part-of, has-part, property-of). Expressing important qualities or traits of a term.
• Aggregational (summation): Logic statement and type of association that indicates summation or aggregational associations that are mutually exclusive, completely exhaustive, no overlap.
• Navigational (parent-child): Logic statement and type of association that is an informal set of relations which are used to navigate from one thing to another thing without defining formal meaning.
• Constraint: Logic statement that describes an axiom, rule, constraint, restriction, or assertion of a structure or model.  Constraints tend to be convertible into IF…THEN…ELSE types of logic statements. Constraints can be connected together by joining restrictions using logic connectors (e.g. AND, OR, NOT, NOR, XOR, NAND).
• Fact: Logic statement about the numbers and words that are described by and instances/individuals of a model.  Facts are differentiated from other facts using aspects (a.k.a. dimensions) which provide explicit context. (a.k.a. instance, individual)

A conceptualization of a logic system can be complete or incomplete (e.g. missing important logic statements); can be consistent or inconsistent (e.g. logic statements contradict one another); can be precise or imprecise (e.g. logic statements are not consistent with reality). A properly functioning logic system is said to be verifiably complete, consistent, and precise.

A conceptualization of a logic system can be adequate or inadequate meaning that the conceptualization tested and validated to yield reliability and accuracy consistent with the specified purpose of the conceptualization's stakeholders. A logic system is said to be adequate if it meets the aim of the stakeholders of that logic system.  Whether a logic system is adequate can be determined and proven via testing of the logic system.

Every logic system is effectively a set of logic statements that is represented in what amounts to a knowledge graph that is human readable and machine readable. This form provides unprecedented clarity with respect to the information represented in the logic system represented by the knowledge graph:

1. a subject which is a noun that represents the thing being related to the object (#3)
2. a predicate which is a verb that represents the type of relationship between the subject (#1) and object (#3)
3. an object which is a noun that represents the thing being related to the subject (#1)

Additional Information:

• Problem Solving Systems
• Practical Ontology Like Things
• Finite Model Theory
• Seattle Method Value Explained (Pillars of Quality and Trustworthiness)
• Modern Accountancy