F-systems are digraphs that enable to model sentences that predicate the falsity of other sentences. The existence of conglomerate guarantees the absence of paradoxes. Conglomerates also enable to characterize referential contradictions.
F-systems are digraphs that enable to model sentences that predicate the
falsity of other sentences. Paradoxes like the Liar and Yablo's can be analyzed
with that tool to find graph-theoretic patterns. In this paper we present the
F-systems model abstracting from all the features of the language in which the
represented sentences are expressed. All that is assumed is the existence of
sentences and the binary relation '... affirms the falsity of ...' among them.
The possible existence of non-referential sentences is also considered. To
model the sets of all the sentences that can jointly be valued as true we
introduce the notion of conglomerate, the existence of which guarantees the
absence of paradox. Conglomerates also enable to characterize referential
contradictions, i.e. sentences that can only be false under a classical
valuation due to the interactions with other sentences in the model. A Kripke's
style fixed point characterization of groundedness is offered and fixed points
which are complete (meaning that every sentence is deemed either true or false)
and consistent (meaning that no sentence is deemed true and false) are put in
correspondence with conglomerates. Furthermore, argumentation frameworks are
special cases of F-systems. We show the relation between local conglomerates
and admissible sets of arguments and argue about the usefulness of the concept
for argumentation theory.