Applying time-dependent algebraic systems for describing situations

NATO Cooperative Cyber Defence Centre of Excellence

“…In this work we consider time-dependent systems. These are systems, where the sets of elements and the properties of and relations between elements are dependent on time (see Lorents, Matsak 2011). At any moment of time t the system M is in a certain state M(t), or in other words, there is a certain situation in the system (see Jakobson 2011).…”

NATO Cooperative Cyber Defence Centre of Excellence

“…Next we must identify the relations Set and Sig, which allow us to relate time moments with sets of elements from class CSets and signatures (or collections of the properties of elements and the relations between elements) from class CPred. Only now can we present the definition of a timedependent system: Definition 3 (Lorents, Matsak 2011). An ordered triplet 〈∇,Set,Sig〉 is called a time-dependent system, if the following condition is fulfilled:…”

“…The development of time-dependent systems, or in Jakobson's terminology -dynamic systems, in real macro world seems to happen according to the following principles (Lorents, Matsak 2011;Lorents 2006;Lorents 1998 The principle of no predestination (The system arriving to a specific state in time moment t is based on chance -it is an event with some probability) -…”

“…These are systems, where the sets of elements and the properties of and relations between elements are dependent on time (see Lorents, Matsak 2011). At any moment of time t the system M is in a certain state M(t), or in other words, there is a certain situation in the system (see Jakobson 2011).…”

“…One option for assessing and comparing plausibility is to use the principle of correlation of developments and deduction, according to which the more logical an inference, where the starting point is the description DesM(t) of the current situation M(t) of the system M and the where the result is the description DesM(t') of a possible following situation M(t'), the more probable it is that this situation develops in the system (see Lorents 1998Lorents , 2006Lorents, Matsak 2011).…”