We show that soft constraints can be used to model logical reasoning, that is deduction and abduction (and induction). In partic- ular, we focus on the abduction process and we show how it can be implemented with a (soft) constraint removal operator. As a running application example throughout the paper, we reason with access control policies and credentials. In this way, we can associate the level of preference de¯ned by the \softness" of the constraint with a \level" of trust. The main bene¯t comes during the process of automated access authorization based on trust: soft constraint operations can be easily adopted to measure the level of trust required for each operation. Moreover, when the level is not su±cient, abduction can be used to compute the missing credentials and the levels that grant the access, making the request a (weighted) logical consequence. The proposed framework can be used to automate the deduction-abduction negotiation processes.