The relational algebra is a procedural query language for relational databases. In this paper we survey extensions of the relational algebra that can query databases recording time-varying data. Such an algebra is a critical part of a temporal DBMS. We identify 26 criteria that provide an objective basis for evaluating temporal algebras, Seven of the criteria are shown to be mutually unsatisfiable, implying there can be no perfect temporal algebra, Choices made as to which of the incompatible criteria are satisfied characterize existing algebras Twelve time-oriented algebras are summarized and then evaluated against the criteria. We demonstrate that the design space has in some sense been explored in that all combinations of basic design decisions have at least one representative algebra. Coverage of the remaining criteria provides one measure of the quality of each algebra We argue that all of the criteria are independent and that the criteria identified as compatible are indeed so, Finally, we list plausible properties proposed by others that are either subsumed by other criteria, are not well defined, or have no objective basis for being evaluated. The algebras realize many different approaches to what appears initially to be a straightforward design task.

The communicating sequential processes (CSP) formalism, introduced by Hoare [Hoa85], is an event-based approach to distributed computing. The action-system formalism, introduced by Back & Kurki-Suonio [BKS83], is a state-based approach to distributed computing. Using weakest-precondition formulae, Morgan [Mor90a] has defined a correspondence between action systems and the failures-divergences model for CSP. Simulation is a proof technique for showing refinement of action systems. Using the correspondence of [Mor90a], Woodcock & Morgan [WM90] have shown that simulation is sound and complete in the CSP failures-divergences model. In this thesis, Morgan's correspondence is extended to the CSP infinite-traces model [Ros88] in order to deal more properly with unbounded nondeterminism. It is shown that simulation is sound in the infinite-traces model, though completeness is lost in certain cases. The new correspondence is then extended to include a notion of internal action. This allows the ...

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The thesis investigates some of the traditional problems with the established formal methods, such as requirements elicitation, the validation problem, divergence from current industrial practice, adverse effects on early problem solving and the incompleteness of perspective. Recent approaches to solving some of these problems are reviewed, including structured and formal methods integration, hybrid formal methods and multi-paradigmed approaches. The definition of a method first used by Kronlof is adopted and two reasons for integrating methods are hypothesised: ffl The integration of methods which result in a richer methodological profile, such as methods which address different stages of the life-cycle, and; ffl The integration of methods which result in a wider overall perspective, and are thus effective over a wider number of prospective problems, such as methods which consider different orthogonal aspects of requirements. Two pieces of work are then presented, one for each hypot...

Abstract. The quotient operation is a standard feature of set theory, where a set is partitioned into subsets by an equivalence relation. We reinterpret this idea for higher order logic, where types are divided by an equivalence relation to create new types, called quotient types. We present a design to mechanically construct quotient types as new types in the logic, and to support the automatic lifting of constants and theorems about the original types to corresponding constants and theorems about the quotient types. This design exceeds the functionality of Harrison’s package, creating quotients of multiple mutually recursive types simultaneously, and supporting the equivalence of aggregate types, such as lists and pairs. Most importantly, this design supports the creation of higher order quotients, which enable the automatic lifting of theorems with quantification over functions of any higher order. 1

this paper we present Extended Real Time Logic (ERTL) [3] as a formal notation for the modelling and analysis of relative and absolute timing properties of hybrid systems. ERTL embeds the discrete time model of RTL into a continuous model provided by the non-negative reals which, together with other extensions, permits the consideration of piece-wise continuous functions through predicates over real valued variables.

This paper reports a case study in the use of proof planning in the context of higher order syntax. Rippling is a heuristic for guiding rewriting steps in induction that has been used successfully in proof planning inductive proofs using first order representations. Ordinal arithmetic provides a natural set of higher order examples on which transfinite induction may be attempted using rippling. Previously Boyer-Moore style automation could not be applied to such domains. We demonstrate that a higher-order extension of the rippling heuristic is sufficient to plan such proofs automatically. Accordingly, ordinal arithmetic has been implemented in Clam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned. We show the synthesis of a fixpoint for normal ordinal functions which demonstrates how our automation could be extended to produce more interesting results than the textbook examples tried so far.

In a previous paper [Low92] we presented two languages based upon timed CSP, with associated semantic models. The first language included biased operators in the syntax, which could be used to model different priorities on actions. The second language extended this by adding a probabilistic choice operator to the syntax; this allowed us to give a semantics which modelled the probabilities of different behaviours occurring. In this paper we aim to extend these two languages, to bring them up to the full expressive strength of timed CSP. We add environments (variable bindings) to our semantics; this allows us to give a more satisfactory model of recursion and allows us to model mutual recursion. Our previous language did not allow us to model communication of values over a channel. We extend our language and semantic model to overcome this. We prove a new property that holds of all behaviours of a process; this basically says that if a process can refuse two actions seperately then it ca...

Decision procedures are algorithms that can reason about the validity or satisfiability of logical formulae in a given decidable theory, and that always terminate with a positive or negative answer.

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive ’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. 1