DeepAI AI Chat
Log In Sign Up

Monadicity of Non-deterministic Logical Matrices is Undecidable

by   Pedro Filipe, et al.
University of Lisbon

The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst finitely characterizing a much wider class of logics, and has proven to be decisive in a myriad of recent compositional results in logic. Crucially, when a finite non-deterministic matrix satisfies monadicity (distinct truth-values can be separated by unary formulas) one can automatically produce an axiomatization of the induced logic. Furthermore, the resulting calculi are analytical and enable algorithmic proof-search and symbolic counter-model generation. For finite (deterministic) matrices it is well known that checking monadicity is decidable. We show that, in the presence of non-determinism, the property becomes undecidable. As a consequence, we conclude that there is no algorithm for computing the set of all multi-functions expressible in a given finite Nmatrix. The undecidability result is obtained by reduction from the halting problem for deterministic counter machines.


page 1

page 2

page 3

page 4


Finite two-dimensional proof systems for non-finitely axiomatizable logics

The characterizing properties of a proof-theoretical presentation of a g...

An unexpected Boolean connective

We consider a 2-valued non-deterministic connective ∧-5.5pt ∨ defined by...

Proof Search on Bilateralist Judgments over Non-deterministic Semantics

The bilateralist approach to logical consequence maintains that judgment...

Coherent Interaction Graphs

We introduce the notion of coherent graphs, and show how those can be us...

An ecumenical view of proof-theoretic semantics

Debates concerning philosophical grounds for the validity of classical a...

History-deterministic Vector Addition Systems

We consider history-determinism, a restricted form of non-determinism, f...

Descriptive Complexity of Deterministic Polylogarithmic Time

We propose a logical characterization of problems solvable in determinis...