Abstract. Linear logic has many properties that make it suitable for application in various areas of computer science. It is able to describe dynamic processes, non-determinism, parallelism on syntactic level. In our paper we try to discuss resource oriented character of linear logic, its possibility to deal with such important resources for computer science as space (memory) and time. Handling with resources takes place in deduction system of linear logic. We show how special form of proofs, called designs, is constructed and we show the relationship between space and time in designs.

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.

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Abstract. Computer science uses still more formal models to aid the understanding of complex software systems and to reason about their behavior, in particular to verify the correctness of a system or at least some desired aspects of its behavior with respect to a formal specification. All these techniques are grounded in formal models of system execution which are themselves rooted in the formal semantics of the underlying programming languages. Denotational semantics expresses the meaning of programs by functions from syntactical domains to semantic domains which can be non-trivial mathematical structures. We present in this document representation of denotational semanitcs based on category theory. We consider memory states as objects of category and semantic functions as morphisms. Category is then a model and semantics of a program written in our language Jane is modeled in this category as a path, i.e. a composition of morphisms.

Abstract. Linear logic appears as a suitable logical system for description of dynamic properties of various network activities in computer science. It disposes with new connectives which create new opportunities to describe properties of real network processes, e.g. parallelism, causality and commutativity of duality between processes. We extend this logic with Aristotelian modalities and we formulate their appropriate model. In our contribution we show how a real network attack can be formalized in this logical system as a polarized game.