我不确定我是否正确理解了您的问题。您似乎想将(整数)属性与每个布尔变量相关联。因此,每个变量都是一对:一个布尔值和一个整数属性。我假设sum
,您的意思是分配给 true 的变量的属性总和。如果是这种情况,您可以通过以下方式在 Z3 中对其进行建模:
;; Enable model construction
(set-option :produce-models true)
;; Declare a new type (sort) that is a pair (Bool, Int).
;; Given a variable x of type/sort WBool, we can write
;; - (value x) for getting its Boolean value
;; - (attr x) for getting the integer "attribute" value
(declare-datatypes () ((WBool (mk-wbool (value Bool) (attr Int)))))
;; Now, we declare a macro int-value that returns (attr x) if
;; (value x) is true, and 0 otherwise
(define-fun int-value ((x WBool)) Int
(ite (value x) (attr x) 0))
(declare-fun x () WBool)
(declare-fun y () WBool)
(declare-fun z () WBool)
;; Set the attribute values for x, y and z
(assert (= (attr x) 2))
(assert (= (attr y) 3))
(assert (= (attr z) 5))
;; Assert Boolean constraint on x, y and z.
(assert (and (value x) (or (value y) (value z))))
;; Assert that the sum of the attributes of the variables assigned to true is greater than 6.
(assert (> (+ (int-value x) (int-value y) (int-value z)) 6))
(check-sat)
(get-model)
(assert (not (value z)))
(check-sat)