Multimodal epistemic Łukasiewicz logics with application in immune system

A longtime season of friendship and scientific collaboration

“…In [17] we extend 3-valued Lukasiewicz logic L 3 to the 3-valued multimodal Lukasiewicz logic E L 3 (n) by adding n unary modal "knowledge" operators i and ♢ i (i = 1, ..., n) to the language of L. We extend 3-valued multimodal Lukasiewicz logic E L 3 (n) to the logic E L 3 (n) by adding global modal (knowledge) operators and ♢ to the language of E L 3 (n).…”

“…We introduced a new logic [17] (2015), a multimodal epistemic Lukasiewicz logic, which is an extension of the infinitely valued Lukasiewicz logic, the language of the logic is extended by unary connectives that are interpreted as modal operators (knowledge operators). We proposed the use of such logic in studying immune system.…”

Dynamic Łukasiewicz logic and its application to immune system

“…Rashevsky has founded relational biology that is the study of biology from the standpoint of definition of relations between the parts of a biological system. An analysis of the biological system as the immune system by relational system using multi-modal epistemic Łukasiewicz logics is given in Di Nola et al (2015), where an estimation of statements and corresponding reasoning is given in three gradations: true, unknown and false. Notice, that the classical multi-modal epistemic logic for multi-agent systems was developed by Porter in (2003).…”

“…In this section, we try to represent some simple fragment of an immune system by n-valued Kripke frame with the following interpretation in immune models that is different, but similar, which has given in Di Nola et al (2015). Now we give a naive definition of immune system I mS. An immune system I mS is a set of T cells with some actions between them.…”

“…Identifying T cell with possible world and an action between T cells with the relation between T cells we can represent an immune system I mS as a n-valued descriptive Kripke frame. A visual presentation as descriptive Kripke frames represented as an immune system can be found in Di Nola et al (2015). We are interested in finite fragment of immune system FragmImS.…”