# Quantales, observational logic and process semantics

@article{Abramsky1993QuantalesOL, title={Quantales, observational logic and process semantics}, author={Samson Abramsky and Steven J. Vickers}, journal={Mathematical Structures in Computer Science}, year={1993}, volume={3}, pages={161 - 227} }

Various notions of observing and testing processes are placed in a uniform algebraic framework in which observations are taken as constituting a quantale. General completeness criteria are stated, and proved in our applications.

## 228 Citations

### Quantales and Observational Semantics

- Mathematics
- 2000

The mathematical framework hitherto available is extended so that it can be applied to more general systems than before, in particular to quantum systems and systems whose behaviour is partially unobservable.

### Relating Algebraic and Coalgebraic Logics of Knowledge and Update

- Philosophy, Computer Science
- 2006

It is shown how by applying a similar approach to Jacob's predicate lifting to the authors' Coalgebra, one obtains the algebraic logic version of dynmic epistemic logic.

### A logical view of composition and refinement

- Computer Science, PhilosophyPOPL '91
- 1991

The Iogics provide a setting for the stud y of composition and refinement rules, and a framework for the use of the modular specification methods that these rules underpin, which arise naturally from extant specification approaches.

### Modular Specification of Concurrent Systems with Observational Logic

- Computer ScienceWADT
- 1998

We present a dynamic form of observational logic for specifying concurrent systems on the basis of their observable behaviour, in particular without needing a language for describing states, which…

### Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras

- Mathematics, Computer ScienceLogica Universalis
- 2022

This work proposes various methods for combining or amalgamating propositional languages and deductive systems and describes quite extensively the relationships among the algebraic and order-theoretic constructions and the corresponding ones based on a purely logical approach.

### Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras

- Mathematics, Computer ScienceLogica Universalis
- 2022

This work proposes various methods for combining or amalgamating propositional languages and deductive systems and describes quite extensively the relationships among the algebraic and order-theoretic constructions and the corresponding ones based on a purely logical approach.

## References

SHOWING 1-10 OF 42 REFERENCES

### A Theory of Communicating Sequential Processes

- Computer ScienceJACM
- 1984

A mathematical model for communicating sequential processes isgiven, and a number of its interesting and useful properties arestated and proved. The possibilities of nondetermimsm are fullytaken into…

### Bisimulation through Probabilistic Testing

- Computer ScienceInf. Comput.
- 1991

### CCS without tau's

- Computer ScienceTAPSOFT, Vol.1
- 1987

It is shown that one can develop an adequate version of CCS which does not use the special combinator τ for internal actions and instead, the choice operator + is replaced by two new choice operators ⊕ and [, representing internal and external nondeterminism respectively.

### Bisimulation can't be traced. Preliminary report

- Computer Science
- 1987

The authors examine what additional operations are needed to explain bisimulation similarly-specifically in the case of finitely branching processes without silent moves, and formulate a general notion of Structured Operational Semantics for processes with Guarded recursion (GSOS), and demonstrate that bisimulations does not agree with trace congruence with respect to any set of GSOS-definable contexts.

### Linear and Branching Structures in the Semantics and Logics of Reactive Systems

- Computer ScienceICALP
- 1985

In this presentation we reviewed the dichotomy between branching and linear views of reactive systems as they are reflected in three different approaches to the formalization of reactive systems.…

### Behavioural Equivalence Relations Induced by Programming Logics

- Computer ScienceICALP
- 1983

This paper compares the descriptive power of three programming logics by studying the elementary equivalence relations which the logics induce on nondeterministic state-transition systems and finds that the notions of bisimilarity, Ogden, and observation equivalence are very strong equivalences compared with those induced by theLogics.

### Algebraic laws for nondeterminism and concurrency

- Computer ScienceJACM
- 1985

The paper demonstrates, for a sequence of simple languages expressing finite behaviors, that in each case observation congruence can be axiomatized algebraically and the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.