public:t-713-mers:mers-23:reasoning-basics
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Table of Contents
DCS-T-713-MERS-2023 Main
Lecture Notes
Introduction to Reasoning in Machines: Basic Concepts
Syllogisms
| What is it? | A form of deductive argument/reasoning in which a conclusion is drawn from 2 given or assumed propositions (premises / statements). The premises and the conclusion are simple declarative statements constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate) E.g. all dogs are animals; all animals have four legs; therefore all dogs have four legs. The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself. (Based on Oxford Dictionary and Encyclopedia Britannica) |
| 3 types | Categorical, conditional and disjunctive. |
| Categorical | The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice. Assumes all premises are true. |
| Conditional | Implies an if in the premises. E.g. You are injured. I am qualified to assist with injuries. I can heal you. |
| Disjunctive | Uses an either/or premise. If it is known that at least one of two statements is true, and that it is not the former that is true; we can infer that it has to be the latter that is true. |
Well-Known Syllogisms
| Moduls Ponens | If a conditional statement if P then Q is accepted, and the antecedent P holds, then the consequent Q may be inferred. E.g. If it's raining then its cloudy. It is raining. Then it's cloudy. |
| Moduls Tollens | A mixed syllogism that takes the form of If P, then Q. Not Q. Therefore, not P. Application of the general truth that if a statement is true, then so is its contrapositive (“if not-B then not-A” is the contrapositive of “if A then B”). |
Boolean Logic
| Number of values | Two: F,T |
| Operators | Conjunction (AND), disjunction (OR), negation (NOT) |
| Combinations of logic gates | XOR, NAND, ANDN, ORN, NOR … Fundamental for all forms of computing. |
Reasoning Methods
| Forward Chaining | A data-driven method of reasoning in which the implications of existing data is deduced until an endpoint (goal) is achieved. Repeated application of modus ponens that can be equated with 'deduction'. Used in expert systems, business and production rule systems. |
| Backward Chaining | A goal-driven reasoning method for inferring unknown truths from known conclusions (goal) by moving backward from a solution to determine the initial conditions and rules. Backward chaining is often applied in artificial intelligence (AI) and may be used along with its counterpart, forward chaining. Repeated application of modus ponens that can be equated with 'abduction'. Used in automated theorem provers, proof assistants, and various artificial intelligence applications. |
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2023©K.R.Thórisson
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