Multi-Valued Preferential Halpern-Shoham logic for relations of Allen and preferences

In this paper a preferential extension of the Halpern-Shoham logic (HS) is proposed. The proposed extension (PHS) may be exploited for a representation of both temporal relations and preferences, which adds some “rationality” for temporal reasoning. The next, a new interval-based fibred semantics will be proposed for some subsystem of PHS with temporal modalities restricted to 〈L〉-operator, denoted by PHS^L. It appears that some ideas of this semantics type can be useful in more practical contexts such as a plan controller construction.