EsoLogic

EsoLogic is an esoteric formal logic created because eso is fun.

Operators
EsoLogic has the standard operators from most formal logics, in a typable format. These include (which are primitive depends on who's defining):
 * : "φ and ψ"- logical conjunction
 * : "φ or ψ"- logical disjunction
 * : "not φ"- logical negation
 * : "if φ then ψ"- implication

In addition, it borrows some things from other logics. For example, Temporal logic:
 * : "Next"- φ holds at the next state
 * : "Global"- φ holds at all future states
 * : "Final"- φ has to hold at some point
 * : "Until"- φ has to hold until ψ does, and can hold beyond.
 * : "Historically"- φ has been true in the past

Fuzzy logic:
 * Truth variables can have "degrees of truth" that are any real number such that 0≤n≤1

Epistemic logic:
 * φ: "τ knows φ"- Agent τ knows that φ is true
 * φ: "τ believes φ"- Agent τ believes that φ is true

Communication epistemic logic:
 * : "Tells"- τ tells υ that Φ (if υ trusts τ, then υ now knows/believes φ) (fails if )

Deontic logic:
 * : "It is obligatory that τ φ"
 * : "It is permissible that τ φ"
 * : "It is forbidden that τ φ" (note that there's an operator collision here with Future)

And more stuff, when it is thought of.