CIS 5603. Artificial Intelligence

Binary Reasoning

Pei Wang

1. Reasoning system

Reasoning (inference) is the process of deriving new knowledge (or beliefs) from existing knowledge following certain general rules.

The study of Logic concerns of valid reasoning, and a logic (system or model) normally consists of

a representation language, usually specified by some grammer rules
the semantic definitions of meaning and truth in the language
a set of valid inference rules on the language

A reasoning system implements the grammar rules and inference rules, maintains a memory structure, and follows a control mechanism.

2. Theorem proving

Theorem proving or automated reasoning: deriving theorems from axioms, with the following typical design.

Language and rules: first-order predicate logic (often known as the "classical logic")
Semantics: model theory ("Snow is white" is true if and only if snow is white)
Implementation: natural deduction or resolution and refutation
Control: heuristic search

Example: Logic Theorist

Applied outside axiomatic systems: use facts or reliable knowledge as axioms. Example: family relation.

3. Induction and abduction

Induction is the inference from specific statements to general statements ("argument from the particular to the universal").

Bacon's method of induction: repeated observations and generalizations.

Hume on induction: induction cannot be justified as valid inference.

Peirce defined induction and abduction as "reversed deduction" (in different ways), and considered their functions as "generalization" and "explanation", respectively.

Inferential Learning Theory: non-deductive reasoning can be considered as learning.

A neural approach to relational reasoning: to treat "reasoning" as function learning.

4. Non-monotonic reasoning

Commonsense reasoning: open system, default assumptions, defeasible reasoning, non-monotonic logic

Representative approaches:

Issues:

multiple inheritance, e.g. Nixon diamond
learning and revising of defaults