Axiomatic specification

Definition 2-1 An axiomatic specification (or specification by axioms) of a procedure for predicate rhi consists of the union of a set of first-order axioms about rhi and the axiomatic specifications of all the non-primitive predicates used in these axioms. 

Example 2-1 A possible axiomatic specification of the memberll problem is ... 

Anyway, whatever the actual setting, the major potential advantage of axiomatic specifications is the following ... 

Since deductive inference is generally a familiar notion, we do not survey it here. We rather directly propose a taxonomy of the different ways of applying deductive inference to program synthesis from axiomatic specifications. Thus, Sections 2.2.1 to 2.2.3 respectively contain general introductions to transformational synthesis, proofs-as-programs synthesis, and schema-guided synthesis. 

In transformational synthesis, a sequence of meaning-preserving transformation rules is applied directly to a specification, until a program is obtained. This kind of stepwise forward reasoning is akin to constructing a derivation tree, and is feasible with axiomatic specifications that link their parameters in a relational way ... 

In Chapter 2, we survey the use of deductive inference in automatic programming. Axiomatic specifications are expected to be complete and non-ambiguous, but are usually also quite lengthy and artificial. Deductive synthesis from axiomatic specifications can be classified into transformational synthesis, proofs-as-programs synthesis (or constructive synthesis), and schema-guided synthesis. We survey the achievements of deductive synthesis of LISP functions and Prolog predicates. 

Where is the model defined and how does it interact with the kernel implementation There are in fact several ways to implement the model and each has its assets and drawbacks. We decided to keep the whole hardware model in the specification-only ghost state. At first sight, with this approach one would face the problem to transfer data between the hardware ghost state and the C state, which VCC forbids. However, one can circumvent this issue via axiomatic specification functions that indirectly assign some value to a C variable by assuming their equality as a postcondition (cf. PPC.assign in Sect. 4.2). 

It is axiomatic that sales analysis depends on detailed records of sales of a specific chemical to a specific company. Paramount to the success of such studies is the existence of data recorded on a systematic and continuous basis. It follows that these studies are done best by an ia-house staff on products already produced by the company. However, on occasion, a product new to the company can be studied by the ia-house group with the assistance of their field sales force. For example, a producer of polypropylene could use its people to secure data on the consumption of other thermoplastics by their customers. Such an exercise might identify opportunities for a new producer, but a more detailed marketing research study would probably be done before entry iato the new product area was made. 

Customer attributes (CAs) can be collected in any number of ways. The key to know is that in axiomatic design, performance and perception expectations are equivalent to CAs, and they are what customers expect from a specific product or service. In other words, CAs come into play when you have a specific solution in mind, and you need to design it in the best way. 

The final step of axiomatic design ensures that you map your design specifications to your process, so it can produce and deliver your new solution, time after time, without mistake. Using the same approach used in translating FRs into DPs, the designer translates each DP into a set of corresponding process variables (PVs). Therefore, if the DP is 0/0/255 on the RGB scale, plus or minus five, then what are the variables in the process that make the part meet this specification These are the related PVs. 

The constructive model P(A(M) SC C )xN) acts as before, as a filter on the prior P(S( -C)x I A) output from the cosmological theory. In this respect, the anthropic bias is indistinguishable from the pruning rule generated by Hoyle but as it is driven by incomplete theoretical specification rather than mere intractability, the posterior distribution is not provisional and cannot act as a constraint on reductionist refinements of N or X It is not a substitute for a theory of particular initial conditions, because it adds nothing axiomatic to the structure of the causal theories represented by... 

Heritability refers not to a trait in isolation but to a trait in a specific population exposed to a specific set of environments— which means the trait may have different heritabilities in different populations in different environments.7 This is axiomatic in the biological sciences, but often ignored in the behavioral sciences. 

It is, of course, axiomatic that one s specific purpose in staining bone and cartilage, the organism s type, size, and age all direct the choice of protocol and how closely to follow it. A number of fixatives for differential staining have generally been employed, most frequently 95% EtOH or 10% formalin... 

Computer-aided automation of process design requires a whole new approach to part manufacture and assembly planning. This centres on the decision logics, formulae, algorithms and data extractions. This approach is labelled as the Generative Method [4]. Examples of such procedures are Decision Trees, Decision Tables, Axiomatic and Expert systems. Regardless of their approach they remain complex in nature and this led to the specific applications, such as those in sheet metal fabrications and electronics manufacture, where parameters are more... 

However, there is one way how to improve the situation code generation. If we generate implementation from the specification, the compliance between them is axiomatic. If we are able to generate enough code from the specification to run into the hand-written business code where we check for the lower-level properties, the conclusions about the component composition are going to hold. 

The use of formal metliods mandates a scientific approach. One possible approach is to formalise specification knowledge as an axiomatic system. Tlie CREATIV toolset uses a new model and a new definition of the specification process, together with an axiomatic theory to support specification knowledge. All operations in tlie system are provable and traceable we have built the reasoning component of tlie CREATIV toolset on the basis of this theory. 

If specification is to be a rigorous discipline, tlien tliere must be a proper scientific approach to tlie subject. We suggest a new approach to specification, in which all specification knowledge is embedded within an axiomatic or rule-based theory, though this theory is nonnally concealed from users. This requires ... 

In summary, our model for specification is based on a network in which a collection of activities is represented by nodes, each of which is linked to others by constraints or business rules, represented by lines or directed arcs. Each activity (node) requires data on which to operate, may involve a computational fimction on that data, and is activated by one or more events. Each activify must obey the business rules (satisfy the constraints) to which it is subject. These rules or constraints are also used to generate additional infonnation by inference. This model will operate according to scientific principles these principles are embedded in a scientific theory. One way, though not tlie only way, of organising such principles, is as an axiomatic system. 

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