Circular reasoning

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Circular reasoning

Good informal arguments offer justification for their conclusions. They go wrong if the justifications double back, rendering the arguments circular. Circularity, however, is not necessarily a single property of an argument, but may depend on (a) whether the argument repeats an earlier claim, (b) whether the repetition occurs within the same line of justification, and (c) whether the claim is p...

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Hierarchical Circular Compositional Reasoning

We describe a composition rule for hierarchically composed components that may involve circular reasoning between the components. It is similar to previous work by McMillan, specialized to component level reasoning. In contrast to McMillan’s work, our composition rule can be used in provers that only support safety properties (e.g. kinduction model checkers) as long as the system and component ...

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Circular Compositional Reasoning about Liveness

Compositional proofs about systems of many components often involve apparently circular arguments. That is, correctness of component A must be assumed when verifying component B, and vice versa. The apparent circularity of such arguments can be resolved by induction over time. However, previous methods for such circular compositional reasoning apply only to safety properties. This paper present...

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A lattice-theoretic framework for circular assume-guarantee reasoning

We develop an abstract lattice-theoretic framework within which we study soundness and other properties of circular assume-guarantee (A-G) rules constrained by side conditions. We identify a particular side condition, non-blockingness, which admits an intelligible inductive proof of the soundness of circular A-G reasoning. Besides, conditional circular rules based on non-blockingness turn out t...

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Inverse circular-circular regression

The problem of determining the values of the independent variable given a value of the dependent variable is commonly referred to as the inverse regression problem. This problem is also encountered in real life with circular data and we refer to it in that context as the inverse circular regression problem. For such a problem, we develop distance-basedmethods, and parametric methods, where we u...

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ژورنال

عنوان ژورنال: Nature

سال: 1988

ISSN: 0028-0836,1476-4687

DOI: 10.1038/332216b0