Finite Countermodel Machine

From Esolang
Jump to navigation Jump to search
Finite Countermodel Machine
Paradigm(s) declarative, logic
Designed by User:Ukeharu
Appeared in 2025
Memory system State-based
Dimensions one-dimensional
Computational class Finite state automata
Reference implementation Unimplemented
File extension(s) .fcm
This is still a work in progress. It may be changed in the future.

Finite Countermodel Machine is an esoteric language designed by User:Ukeharu in 2025, based on relational models of modal logic and tableaux derivations. The language makes use of proof searching with tableaux to generate finite state automata that then run on a string given either at run-time or compile-time. The language requires both an understanding of proof theory and modal logics if one wishes to avoid intractable proof searches, which combined with the complexity of visualising how the premises of the tableaux proof relate to the final output, makes the language non-trivial to use without background knowledge.

Language Description

Modal Logic

Relational Semantics

Tableaux Derivations

Generating Countermodels

Finiteness of Tableaux Derivations

Decision Process

Decidability

Countermodels as Finite State Automata

Possible Worlds as Finite States

State Transitions

Halting States

Sample Programs

External Resources

Wikipedia article on relational models

Wikipedia artible on tableaux proofs