Reading on Formal and Cognitive Semantics

semantic function to the concrete semantics, which are embodied onto the 1 changes of status of a finite set of variables constituting the semantic environment 2 of computing. 3 The theoretical foundations of deductive semantics are based on process alge4 bra and Boolean partial differentials [62, 63]. Based on the mathematical models 5 and architectural properties of a program at different composing levels, deductive 6 models of software semantics, semantic environment, and semantic matrix will be 7 formally defined. Properties of software semantics and relations between the soft8 ware behavioral space and semantic environment will be elaborated in Sec. 3.3. A 9 comprehensive analysis of the deductive semantics of Real-Time Process Algebra 10 (RTPA) may be referred to [58, 60, 63]. 11 Deductive semantics can be used to define both the abstract and concrete 12 semantics of large-scale software systems, facilitate software comprehension and 13 recognition, support tool development, enable semantics-based software testing and 14 verification, and explore the semantic complexity of software systems. 15 This subsection develops the mathematical models of deductive semantics. The 16 deductive models of semantics, semantic function, and semantic environment at var17 ious composing levels of programs are introduced. Properties of software semantics 18 and relationships between the software behavioral space and the semantic envi19 ronment are studied. New methods such as the semantic differential and seman20 tic matrix are developed to facilitate deductive semantic analyses from a generic 21 semantic function to a specific semantic matrix, and from semantics of statements to 22 those of processes and programs. The establishment of the deductive semantic rules 23 of RTPA may be referred to [67], where deductive semantics of a comprehensive set 24 of software processes is modeled. 25 3.2.1. The mathematic model of software semantics 26 A semantic environment of a program in a given programming language is a logi27 cal model of a finite set of identifiers and their values changing over time along the 28 execution of the program. The semantic environment constituting behaviors of soft29 ware is inherently a three-dimensional structure known as the operations, memory 30 space, and time. 31 Definition 19. The behavioral space Ω of a program executed on a certain machine is a finite set of variables operated in a 3-D state space determined by a triple, i.e.: Ω ∧ = (OP , T, S) (9) where OP is a finite set of operations, T is a finite set of discrete steps of program 32 execution, and S is a finite set of memory locations or their logical representations by 33 identifiers of variables. The set of variables of a program, S, plays an important role 34 1st Reading October 1, 2010 11:49 WSPC/S1793-351X 214-IJSC SPI-J091 00083