Reflective algorithms are algorithms that can modify their own behaviour. Recently a behavioural theory of reflective algorithms has been developed, which shows that they are captured by reflective abstract state machines (rASMs). Reflective ASMs exploit extended states that include an updatable representation of the ASM signature and rules to be executed by the machine in that state. Updates to the representation of ASM signatures and rules are realised by means of a sophisticated tree algebra defined in the background of the rASM. In this article the theory is taken further by an extension of the logic of ASMs, by means of which we can formally express properties a reflective algorithm must satisfy. The proof theory associated with the logic then enables static verification of adaptive systems. The key is the introduction of terms that are interpreted by ASM rules stored in some location. We show that fragments of the logic with a fixed bound on the number of steps preserve completeness, whereas the full run-logic for rASMs becomes incomplete.

反射算法是可以修改自己行为的算法。最近开发了反射算法的行为理论，表明它们被反射抽象状态机 (rASM) 捕获。反射 ASM 利用扩展状态，其中包括 ASM 签名的可更新表示和该状态下机器要执行的规则。ASM 签名和规则表示的更新是通过在 rASM 背景中定义的复杂树代数来实现的。在本文中，该理论进一步扩展了 ASM 的逻辑，通过它我们可以形式化地表达反射算法必须满足的属性。然后，与逻辑相关的证明理论可以对自适应系统进行静态验证。关键是引入了由存储在某个位置的 ASM 规则解释的术语。我们展示了具有固定步数限制的逻辑片段保持完整性，而 rASM 的完整运行逻辑变得不完整。