Abstract Justification theory is a general framework for the definition of semantics rule-based languages that has high explanatory potential. Nested justification systems, first introduced by Denecker et al. , allow composition systems. This notion nesting thus enables modular languages, and increases representational capacities theory. As we show in this paper, original characterization neste...

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear nested systems. Moreover, we show a semantical characterisation of intuitionistic, multi-modal and non-normal modal logics for all these systems, via a case...

The progress in computer simulation tends to simulate complex systems governed by “internal models”, i.e. sophisticated activities of computing technique in real time flow. Independently of that, computer simulation needs the object-oriented programming and the agent-based paradigm for constructing “external models” of complex systems that are being designed. Thus the progress tends to use mode...