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&ψ: "φ and ψ"- logical conjunction
• φ|ψ: "φ or ψ"- logical disjunction
• ~φ: "not φ"- logical negation
• φ->ψ: "if φ then ψ"- implication

In addition, it borrows some things from other logics. For example, Temporal logic:

• Xφ: "Next"- φ holds at the next state
• Gφ: "Global"- φ holds at all future states
• Fφ: "Final"- φ has to hold at some point
• φUψ: "Until"- φ has to hold until ψ does, and can hold beyond.
• Hφ: "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:

• Kτφ: "τ knows φ"- Agent τ knows that φ is true
• Bτφ: "τ believes φ"- Agent τ believes that φ is true

Communication epistemic logic:

• Tτ,υΦ: "Tells"- τ tells υ that Φ (if υ trusts τ, then υ now knows/believes φ) (fails if ~Kτφ)

Deontic logic:

• Oτφ: "It is obligatory that τ φ"
• Pτφ: "It is permissible that τ φ"
• Fτφ: "It is forbidden that τ φ" (note that there's an operator collision here with Future)

And more stuff, when it is thought of.