GPFCSP formalization using ŁП1 over 2 logic

Priority is generally viewed as the importance level of an object among others and it is often used in real time systems. GPFCSP is a fuzzy constraint satisfaction problem (FCSP) in which the notion of priority is introduced. The syntax of ŁП1 over 2 logic is powerful enough to formally express prioritized queries. As it is usual in the applications of the interpretation method (at least it is the case when we use propositional logics), propositional letters carry additional structure. In our case, propositional letters will have the form (v, ρ), v and ρ, where v represents the local satisfaction degree and ρ represents its priority. Prioritized formulas are ŁП1 over 2-formulas of the form α((v
1
, ρ
1
), …, (v
n
, ρ
n
)).