The beliefs of the agents in a multi-agent system have been formally modelled in the last decades using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they commit us to model agents that are logically omniscient. We propose a way of avoiding this problem, using a new kind of entities called subjective situations. We define a new doxastic logic based on these entities and we show how the belief operators (...) have some desirable properties, while avoiding logical omniscience. A comparison with two well-known proposals (Levesque's logic of explicit and implicit beliefs and Thijsse's hybrid sieve systems) is also provided. (shrink)

Logicians treat assertions as true, believed or merely hypothesized sentences. The reasoner who uses them, however, is the sole referee who can validate their truth, their aptness to describe an actual situation, their strength (as beliefs) or the relevance of their use in the current logical context. Moreover, the reasoner actively counts on these factors, as part of the reasoning process itself, and should normally be capable, when asked to do so, to assign consistently relative strengths to the assertions used. (...) The paper assumes, first, that assertions have -each- an associated, measurable strength, and that, second, this strength has significant -and measurable- effects on the truth of the sentences, the validity of the conclusion and the soundness of the reasoning. The concepts and formulas required for this are explored, and a semantics and proof theory for a sentential calculus of assertions are proposed as a natural extension of ordinary two-valued reasoning. The resulting theory, though reminiscent of Probability,is autonomous, self-contained and of a purely logical nature. (shrink)