Introduction to Reasoning Machines

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.

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”).

Number of values	Two (True, False)
Atomic Operators	Conjunction (AND), disjunction (OR), negation (NOT)
Combination of Rules	XOR, NAND, ANDN, ORN, NOR … Fundamental for all forms of computing.

Consists of	A set of rules A working memory (WM) An inference engine
Rules	Expressed in some machine-readable way. Each rule consists of n patterns.
WM	Stores the information that the inference engine is working on at any point in time.
Inference Engine	Matches rules against elements in WM.
Match	When a rule matches an element in WM it fires, which means that the system implements what the rule says should happen.

Matching	Pattern matching is the main method that reasoning systems use in their operation. It works along these lines (arrow means output; data stores are in brackets; everything else is processes): [WM] → [Data, Rules] → MATCH → [Output-1 (Conflict Set)] → RESOLVE → EXECUTE → [Output-2] → [WM]
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.

Deduction	Figuring out the implication of facts (or predicting what may come). General → Specific. Producing implications from premises. The premises are given; the work involves everything else. Conclusion is unavoidable given the premises (in a deterministic, axiomatic world).
Abduction	Figuring out how things came to be the way they are (or how particular outcomes could be made to come about, or how particular outcomes could be prevented). The outcome is given; the work involves everything else. Sherlock Holmes is a genius abducer.
Induction	Figuring out the general case. Specific → General. Making general rules from a (small) set of examples, e.g. 'the sun has risen in the east every morning up until now, hence, the sun will also rise in the east tomorrow.
Analogy	Figuring out how things are similar or different. Making inferences about how something X may be (or is) through a comparison to something else Y, where X and Y share some observed properties.