Question

这是我的程序，当图中有一个循环时返回SAT，而在没有循环时返回UNSAT：

(set-option :fixedpoint.engine datalog) 

(define-sort s () Int) 

(declare-rel edge (s s)) 
(declare-rel path (s s)) 

(declare-var a s) 
(declare-var b s) 
(declare-var c s) 

(rule (=> (edge a b) (path a b)))
(rule (=> (and (path a b) (path b c)) (path a c)))

(rule (edge 1 2))
(rule (edge 2 3))


(declare-rel cycle (s))
(rule (=> (path a a) (cycle a)))
(query cycle :print-answer true)

我想在没有周期的情况下获得模型（UNSAT）。我意识到我应该使用命令（get-unsat-core）并将选项设置为（set-option：produce-unsat-cores true）：

(set-option :fixedpoint.engine datalog) 
(set-option :produce-unsat-cores true)
(define-sort s () Int) 

(declare-rel edge (s s)) 
(declare-rel path (s s)) 

(declare-var a s) 
(declare-var b s) 
(declare-var c s) 

(rule (=> (edge a b) (path a b)) P-1)
(rule (=> (and (path a b) (path b c)) (path a c)) P-2)

(rule (edge 1 2) E-1)
(rule (edge 2 3) E-2)
(rule (edge 3 1) E-3)

(declare-rel cycle (s))
(rule (=> (path a a) (cycle a)))
(query cycle :print-answer true)


(get-unsat-core)

我收到此错误：

unsat
(error "line 24 column 15: unsat core is not available")

Answer 1

在unsat情况下获取模型没有任何意义。从字面上无法满足意味着没有模型可以满足您的约束。请针对您要实现的目标发布一个更明确的问题。

unsat核心是有冲突的断言的子集。根据定义，此集合是不能令人满意的，并且不构成您要寻找的模型。此外，我非常怀疑定点引擎是否支持unsat-core，因此，您收到的错误消息只是意味着它们没有被计算。

Answer 2

如果我可能要入侵，则 AFAIK 可能需要命名，以限制要检索unsat core的约束。

smtlib网站提供以下示例：

; Getting unsatisfiable cores
(set-option :produce-unsat-cores true)
(set-logic QF_UF)
(declare-const p Bool) (declare-const q Bool) (declare-const r Bool)
(declare-const s Bool) (declare-const t Bool)
(assert (! (=> p q) :named PQ))
(assert (! (=> q r) :named QR))
(assert (! (=> r s) :named RS))
(assert (! (=> s t) :named ST))
(assert (! (not (=> q s)) :named NQS))
(check-sat)
; unsat
(get-unsat-core)
; (QR RS NQS)
(exit)

@LeventErkok指出，仅当公式为sat时模型可用，而unsat core仅当公式为unsat时可用。

（get-unsat-core）Z3：unsat核心不可用

2 个答案: