Semantics and Algebra for Action Logic Monitoring State Transitions

This position paper is concerned with aspects of an interactive state transition system (based on abstract state machine) by means of the state monitoring in action logic (as multi-modal logic), towards a step to the design for complex systems. Logical models are here presented as theories for implementation design on iDevice, with respect to the algebraic structure caused by state transitions. As a simpler design of complex AI, the environmental constraint is captured as a state, where the function applications are available at each state with the transition to the next states. For communication to the state, and function applications at the state, multi-modal logic model may be of use, where the formula or the condition monitors the state. Then interaction availability is significant, expressed in some algebra on the basis of the meaning definitions for formulas (conditions). By the state transition system, URL searching operations are now formally considered as in algebraic structure. The application of predicates to the states is regarded as applications of functions (transforming conditions) such that its algebraic structure may be given.