# Non-deterministic semantics for quantum states

## TL;DR

This paper introduces a non-deterministic semantic framework for quantum states by leveraging N-matrix theory, providing a logical interpretation of quantum and post-quantum probabilistic models.

## Contribution

It applies non-deterministic semantics to quantum states, offering a new logical foundation and extending to post-quantum theories based on orthomodular lattices.

## Key findings

- Quantum states can be represented as valuations in non-deterministic truth tables.
- The framework provides a natural interpretation of quantum states through non-deterministic semantics.
- Extension to post-quantum models enables logical analysis of broader probabilistic theories.

## Abstract

In this work we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated to infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.