• Fractional semantics
• Beliefs
• Supraclassical logic
• Logic
• Classical logic

The purpose of this thesis is to explore one of the possible evolution of the fractional semantics for classical logic, firstly introduced by Piazza and Pulcini in an article named ``Fractional semantics for classical logic'' (2020). The main idea was born reflecting on the possibilities that a fractional semantics is able to open in the fields of reasoning, natural language and artificial intelligence. Fractional semantics for classical logic has broken the symmetry between tautologies and contradictions considering not only the truthfulness (1) and the falsity (0), but also every rational number between them. The system here presented adds the possibility to have a dialogue between the logic and the world, considering sets of beliefs, but maintaining important logical properties. The system could be useful for further developments about decision in artificial intelligence.