The paper proposes a mathematical programming (MP) approach to solving problems of logical inference in expert or other knowledge-based systems. The propositions that make up the knowledge base of the system are represented as constraints of the MP problem. Variables in the MP problem play the role of atoms in propositional logic. Based on the fact that the domain of each variable is \(\{\) 0,1\(\}\) it is shown that a clause \(C=X_ 1\vee...\vee X_ n\) can be represented as a constraint of the form \(\sum^{n}_{i=1}X_ j\geq 1.\) Furthermore, if \(P_ 1,..., P_ q\) is a collection of premises involving the atoms \(X_ 1,..., X_ n\), the fact that \(X_ k\) logically follows from the premises can be expressed as the MP problem; \(Q=\min X_ k\) subject to the set of linear inequations \(I_ 1,..., I_ q\), one for each premise, and \(X_ i\in \{0, 1\}\), for \(i=1,..., n\). A promising application of this approach is in reasoning using default or other non-monotonic knowledge. A canonical default rule is a proposition of the form: ``if A and we have failed to show the firing is blocked then assume C''. A scheme is suggested for implementing default reasoning in the framework of MP. The MP algorithm for finding the optimal solutions is discussed on some examples. Of particular significance is the ability of the proposed approach to handle knowledge bases in which there are multiple default rules.