# Rules of Logical Inference

*[The Rules of inference are tools of reasoning. They are a list of ways to move from a given premise to a valid conclusion.]*

**Modus Tollens**

"The way that denies by denying"

Modus Tollens moves from one point to another by negating a conclusion that has been made in one of its premises.
Advancing in a negative direction can mostly easily be respresented by movement that is backwards in relation to a character's gaze.
Modus Tollens moves it's legs in graceful sweeping arches away from its forward gaze.

**P∴Q,∼Q,∴∼P**

Modus Tollens consists of two premises.

1) For a given antecedent P there follows a consequent Q

2) Q is negated (False).

Modus Tollens asserts that in this situation one can logically infer that P is also False.

**Disjunctive Syllogism**

"Disjunction Elimination"

The Disjunctive Syllogism explores two paths of progress, but once one of these paths has been eliminated, it moves forward along the other.
Its long nose helps it search for precious resources in a philosophical wasteland.

**P∨Q,∼P∴Q**
1) For the junction P or Q,

2)if not P then Q

3) If not Q then P

Disjunctive Syllogism allows only for one path to exist when it is presented as one of two mutually exclusive pathways.

**Dilemma**

"Double Proposition"

The Dilemma follows two branches of a bifurcated path that eventually reunite. It's actual trajectory is
indeterminate (like schrodinger's cat) and irrelevant because the outcome of its journey is the same.

**P∨Q,∼P∴R,Q∴R,∴R**
1)For the junction P or Q

2)P implies R

3)Q implies R

4)Therefore P or Q yields R or R

The Dilemma is a bifurcating path of logic that reunites at one conclusion.

## Other Rules of Inference

**Modus Ponens**

Reasoning in its most linear form.

1)If P then Q,

2)P, Therefore Q.

**Hypothetical Syllogism**

Equally Linear but less direct.

1) If P then Q,

2)if Q then R,

3)P therefore R.