Intrusion detection system episteme

Abstract

In our paper we investigate the possibilities of modal logics in coalgebras of program systems. We deal with a simplified model of an intrusion detection system. We model an intrusion detection system as a coalgebra and construct its Kripke model of coalgebraic modal linear logic using powerset endofunctor. In this model we present our idea how a fragment of epistemic linear logic can provide knowledge and belief of intrusion attempt.

Coalgebraic modeling of IDS behavior

“…MODELING OF THE IDS BEHAVIOR VIA COALGEBRA OF POLYNOMIAL ENDOFUNCTOR Another aim of our approach of a formal description of the IDS is modeling of its behavior by coalgebra of polynomial endofunctor [7]. For formulating this approach it is necessary to make these steps:…”

“…1. Many-typed signature of packet structure [7] Please note that the content of the signature fragment above is adjusted to example bellow IV-E.…”

What about Linear Logic in Computer Science?

“… Extending linear logic with modal operators of necessity and possibility we have used modal linear logic for reasoning about the observable behavior of programs [13];…”

“… Extending linear logic with epistemic operators of knowledge and belief we obtained epistemic linear logic useful for achieving experiences about incomming network intrusions based on a natural manner of causalities [13], [14].…”

Between syntax and semantics of resource oriented logic for IDS behavior description

“…We model this behavior by coalgebras where IDS is modelled as a coalgebra for an appropriate polynomial endofunctor defined in the abstract frame of category theory [6]. In [5,7] is presented linear logic [8][9][10] extended with epistemic modalities -epistemic linear logic for formal description how objective knowledge and rational belief can be formulated in resource-oriented formula in Kripke's model of possible worlds through extensional satisfaction relation.…”