Universidade Federal do Rio Grande do Norte
Abstract: It is perhaps not so widely known as it should be that any normal modal logic may be presented in a language containing, besides a classic-like implication, a paraconsistent negation whose interpretation dualizes that of intuitionistic negation. Taking such sort of negative modalities seriously, it is also worth noting that modal languages containing them on top of the usual language of distributive lattices may be studied that cover the main classes of Kripke models, and in some such classes no classical negation (nor deductive implications) happen to be definable. In this talk I will review what it means for a connective to be called a negative modality, illustrate how paraconsistent and paracomplete modal negations may interact with one another, extend the approach so as to express modal connectives that allow for negation-consistency and for negation-determinedness to be recovered, and show how several logics with such languages may be presented by way of appropriate standard analytic sequent calculi.
Universiteit van Amsterdam
Abstract: The talk, based on a series of works together with Chenwei Shi and Sonja Smets ("Argument-based Belief in Topological Structures", "Beliefs Based on Evidence and Argumentation"), presents a logical system that combines a topological extension of evidence models ("Justified Belief and the Topology of Evidence") with tools from abstract argumentation theory ("On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games"). The system uses evidence models for representing the information an agent has collected/inferred about which is the real world, and uses abstract argumentation theory for selecting the sets of evidence that defines the agent's beliefs. The talk will focus on the basic ideas of the two involved frameworks, discussing how they are combined to define two types of beliefs, and the properties of the resulting notions.