In this article we shall construct intuitionistic analogues to the main systems of classical tense logic. Since each classical modal logic can be gotten from some tense logic by one of the definitions(i) □ p ≡ p ∧ Gp ∧ Hp, ◇p ≡ p ∨ Fp ∨ Pp; or,(ii) □ p ≡ p ∧ Gp, ◇p = p ∨ Fp(see [5]), we shall find that our intuitionistic tense logics give us analogues to the classical modal logics as well.We shall not here discuss the philosophical issues raised by our logics. Readers interested in the intuitionistic view of time and modality should see [2] for a detailed discussion.In §2 we define the Kripke models for IKt, the intuitionistic analogue to Lemmon's system Kt. We then prove the completeness and decidability of this system (§§3–5). Finally, we extend our results to other sorts of tense logic and to modal logic.In the language of IKt, we have: sentence-letters p, q, r, etc.; the (intuitionistic) connectives ∧, ∨, →, ¬; and unary operators P (“it was the case”), F (it will be the case”), H (“it has always been the case”) and G (“it will always be the case”). Formulas are defined inductively: all sentence-letters are formulas; if X is a formula, so are ¬X, PX, FX, HX, and GX; if X and Y are formulas, so are X ∧ Y, X ∨ Y, and X → Y. We shall see that, in contrast to classical tense logic, F and P cannot be defined in terms of G and H.

Alle Begriffe, in denen sick ein ganzer Prozefi semiotisch zusammenfafl4 entziehen sick der Definition; definierbar ist nur das, was keine Geschichte hat.' The following Article attempts to describe and defend a new approach to the study of foreign law. The core idea is easy to state, although surprisingly difficult to carry out; we shall find that it leads through numerous briar patches before culminating in new and unexpected landscapes. Briefly put, the central claim is this: if comparative law is appropriately combined with legal philosophy the result is a substantially new discipline, "comparativejurisprudence," which is capable of furnishing, not just new knowledge, but a new kind of knowledge about foreign legal systems. Strange to say, comparative lawyers have neglected to scrutinize the foundations of their discipline or to think with sufficient rigor about the essentially philosophical question: How can we best come to understand law in cultures other than our own? And this neglect has impoverished the entire subject. Indeed, as one leafs through the journals one encounters a malaise that is scarcely to be found in any other branch of the law. Comparative law, as we shall shortly see, is said by its leading scholars to be superficial and unsystematic, dull and prone to error. In part this malaise is the product of disappointed hopes; for if any subject in the legal curriculum promises to bring home the Wealth of the Indies, it is comparative law. The variability of law from culture to culture and from age to age is an epic theme, and should be a bugle call to scholarship. Alan Watson, perhaps the deepest critic of the subject, recalls that the idea of comparative law fascinated him since he began to study law: "My notion was that the study of legal developments in a number of states would, by uncovering patterns and divergences, best reveal societal concerns, and how law responds." 2 But he quickly discovered that the subject was bent on other goals. "Needless to say," he observed, "when, as a beginning student, I read the ' "All concepts in which an entire process is semiotically summed up elude definition; only that which has no history can be defined." FRIEDRICH NIETZSCHE, ZUR GENEALOGIE DER MORAL, pt. II, § 13 (Leipzig, C.G. Naumann 1887). In this Article translation credit for substantial quotations is given in footnote parentheticals; shorter quotations have been translated by the author sub silentio, as here.

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We examine local area network protocols and verify the correctness of two representative algorithms using temporal logic. We introduce an interval temporal logic that allows us to make assertions of the form "in the next k units, X holds." This logic encodes intuitive arguments about contention protocols quite directly. We present two proofs of an Ethernetlike contention protocol, one using the interval temporal logic and one using classical temporal logic. We also verify a contention-free protocol using an invariant that seems to have ' wide applicability for such protocols. Section 1: N e t w o r k A s s u m p t i o n sIn this paper we examine typical local area network protocols and verify the correctness of two representative algorithms using temporal logic. The examination is actually bidirectional. On one hand we prove the correctness of two algorithms that are typical of local area network protocols. On the other, we examine the adequacy of the temporal logic formalism as a tool for verifying algorithms that depend strongly on the lengths of transmission delays.The conclusions we would like to draw from this double examination can be summarized as follows:First, it is possible and hence highly recommendable to construct formal proofs of carrier-sense network protocols. Furthermore, the proofs are readable and highlight the intuitive principles underlying the protocols.Second, the classical temporal approach, as presented say in [MP] and [OL], can be applied even to systems which depend on delays of specific lengths. In order to do this, various auxiliary variables and counters have to be added to the state. This requirement of augmentation by auxiliary variables in order to perform concurrent verification is well-known and has been observed in several previous works, e.g., [OG] and [HO]. (See also [Cli] and [Cla].)As an alternative to the addition of auxiliary variables which sometimes amounts to the explicit introduction of a global clock, we consider an extension of temporal logic. This extension enables us to formalize statements such as "in m time units from now X". As a basis to the extended logic, we have adopted a subset of Kr6ger's LAR system [Kr], which we further extend to be able to speak about bounded intervals (see [Mos] , [HMM] , [SMV] , and [KVdR] , for a related approach to different problems).The advantage in using our quantified interval logic is that it can directly formalize intuitive arguments one would make in reasoning about delay-dependent algorithms. Another obvious advantage is eliminating the need for auxiliary variables.On the other hand, the advantage of using the classical temporal logic approach is its neat division of properties into invariance (safety) and liveness properties. In addition, there is the principle of using the simplest formalism that will accomplish the task.In this paper, we present two proofs based on classical temporal logic and one based on the qualified interval logic we have developed. In this way, we hope to illustrate to the reader the distinctive...