Classification of Logics

Logic is a structured way of reasoning. It allows us to draw valid conclusions, make decisions, and solve problems. In AI and Machine Learning ML, logic is essential. It helps systems understand information and make decisions in a reliable way. This chapter explores how logic is classified into formal, informal, and semi-formal types, along with other useful categories like deductive, modal, and fuzzy logic.

What Is Logic?

Logic is the study of reasoning — deciding what is true or false, and how to connect facts to reach conclusions.

Example of simple logic:

• Fact 1: All cats are animals.

• Fact 2: Luna is a cat.

• Conclusion: Luna is an animal.

This is how logical reasoning works: using known facts to learn something new. AI systems do this in different ways, depending on the type of logic used.

Basic Classifications of Logic

On of the possible ways of classification of logics is by structure: Formal, Informal and Semi-Formal

• Formal Logic Formal logic (also called symbolic or mathematical logic) follows strict rules and uses symbols to represent ideas. It is highly structured and easy to verify by a computer.

• Informal Logic Informal logic is how people reason in everyday life. It’s based on language, experience, and common sense rather than symbols or strict steps.

• Semi-Formal Logic Semi-formal logic combines elements of both formal and informal logic. It uses structured rules but allows for uncertainty and natural language interpretation.

Why This Classification Matters in AI & ML

Each type of logic supports a different kind of AI system:

Logic Type	Best For
Formal	Systems needing certainty and provable rules (e.g. robots, theorem solvers)
Informal	Human-like understanding (e.g. chatbots, language models)
Semi-Formal	Decisions under uncertainty (e.g. expert systems, legal AI)

Other Important Classifications of Logic

Beyond the basic categories, logic can also be divided into specialized types used across AI, mathematics, and computer science.

By Reasoning Direction

• Deductive Logic: Goes from general to specific. If the rules are true, the conclusion must be true. Example:

  • All mammals breathe air.

  • Whales are mammals.

  • → Whales breathe air.

  • Used in: Programming, theorem provers, knowledge bases

• Inductive Logic: Goes from specific to general. It creates general rules from observations. Example:

  • This apple fell.

  • That apple fell.

  • → All apples fall.

  • Used in: Machine learning, pattern recognition, AI training

By Update Behavior

• Monotonic Logic: Adding new facts doesn’t change earlier conclusions. Example:

  • All birds fly.

  • Tweety is a bird.

  • → Tweety flies.

  Problem: Doesn’t handle exceptions like penguins.

• Non-Monotonic Logic: Allows earlier conclusions to change with new information. Example:

  • Birds usually fly.

  • But now we learn Tweety is a penguin.

  • → Update: Tweety does not fly.

  Used in: Real-world AI systems with incomplete or changing information

By Modality

• Modal Logic: Adds terms like “must,” “might,” and “possibly.” Used for reasoning about obligations, beliefs, or future events. Operators:

  • □ = necessarily

  • ◇ = possibly

  Example:

  • “The robot must stop if an obstacle is detected.” (□ Stop)

  • “It might rain tomorrow.” (◇ Rain)

  Used in: AI planning, simulation, robotics, security modeling

• Non-modal logic: Does not include such modal operators, focusing purely on truth values.

By Degree of Truth

• Fuzzy Logic: Deals with degrees of truth. Not just true or false, but in between (e.g., 0.7 true). Example:

  • Temperature is not just “hot” or “cold,” but “70% hot”

  • “The room is somewhat clean.”

  Used in: Smart devices, natural language processing, image analysis

• Non-fuzzy (Crisp) logic: (aka Classical or Boolean Logic) Only allows absolute truth values — either 0 (false) or 1 (true).

By Time Awareness

• Temporal Logic: Adds time-based reasoning (before, after, always, eventually). Example:

  • “The system should always log out users after 10 minutes.”

  • “The alarm must ring before the door opens.”

  Used in: Scheduling, process verification, real-time systems

• Non-temporal Logic: Assumes that truth values are timeless or static — they don’t change over time.

Summary Table

Logic Type	Description	Used In
Formal	Rule-based, symbolic, provable	Programming, theorem proving
Informal	Natural, flexible, based on context	Chatbots, conversation, essays
Semi-formal	Mixed, structured with some flexibility	Legal tech, expert systems
Deductive	General to specific reasoning	Rule engines, compilers
Inductive	From data to general patterns	Machine learning
Monotonic	Stable reasoning that doesn’t change	Classical logic systems
Non-monotonic	Adaptive reasoning that updates with new info	Dynamic knowledge bases
Modal	Reasoning about possibility and necessity	Planning, simulation, robotics
Fuzzy	Reasoning with degrees of truth	Smart systems, fuzzy controllers
Temporal	Logic with time-based conditions	Scheduling, automation, real-time AI