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The persisting gap between the formal and the informal mathematics is due to
an inadequate notion of mathematical theory behind the current formalization
techniques. I mean the (informal) notion of axiomatic theory according to which
a mathematical theory consists of a set of axioms and further theorems deduced
from these axioms according to certain rules of logical inference. Thus the
usual notion of axiomatic method is inadequate and needs a replacement.Comment: 54 pages, 2 figure
A System for Deduction-based Formal Verification of Workflow-oriented Software Models
The work concerns formal verification of workflow-oriented software models
using deductive approach. The formal correctness of a model's behaviour is
considered. Manually building logical specifications, which are considered as a
set of temporal logic formulas, seems to be the significant obstacle for an
inexperienced user when applying the deductive approach. A system, and its
architecture, for the deduction-based verification of workflow-oriented models
is proposed. The process of inference is based on the semantic tableaux method
which has some advantages when compared to traditional deduction strategies.
The algorithm for an automatic generation of logical specifications is
proposed. The generation procedure is based on the predefined workflow patterns
for BPMN, which is a standard and dominant notation for the modeling of
business processes. The main idea for the approach is to consider patterns,
defined in terms of temporal logic,as a kind of (logical) primitives which
enable the transformation of models to temporal logic formulas constituting a
logical specification. Automation of the generation process is crucial for
bridging the gap between intuitiveness of the deductive reasoning and the
difficulty of its practical application in the case when logical specifications
are built manually. This approach has gone some way towards supporting,
hopefully enhancing our understanding of, the deduction-based formal
verification of workflow-oriented models.Comment: International Journal of Applied Mathematics and Computer Scienc
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