There are two intuitive principles governing belief formation and argument evaluation that can potentially clash. After arguing that adopting them unrestrictedly leads to an infinite regress, we propose a formal framework in which qualified versions of both principles can be subscribed without falling into such a regress. The proposal integrates tools from two different traditions: structured argumentation and awareness epistemic logic. We show that our formalism satisfies certain rationality postulates and argue that the rest of them can be seen as too ideal when modelling resource-bounded agents.

We introduce the syntax, semantics, and an axiom system for a PDL-based extension of the logic for order of magnitude qualitative reasoning, developed in order to deal with the concept of qualitative velocity, which together with qualitative distance and orientation, are important notions in order to represent spatial reasoning for moving objects, such as robots. The main advantages of using a PDL-based approach are, on the one hand, all the well-known advantages of using logic in AI, and, on the other hand, the possibility of constructing complex relations from simpler ones, the flexibility for using different levels of granularity, its possible extension by adding other spatial components, and the use of a language close to programming languages.

Two classical semantical approaches to studying logics which combine time and modality are the T /spl times/ W-frames and Kamp-frames (Thomason (1984)). In this paper we study a new kind of frame that extends the one introduced in Burrieza et al. (2002). The motivation is twofold: theoretical, i.e., representing properties of the basic theory of functions (definability); and practical, their use in computational applications (considering time-flows as memory of computers connected in a net, each computer with its own clock). Specifically, we present a temporal /spl times/ modal (labelled) logic, whose semantics are given by ind-functional frames in which accessibility functions are used in order to interconnect time-flows. This way, we can: (i) specify to what time-flow we want to go; (ii) carry out different comparisons among worlds with different time measures; and (iii) define properties of certain kinds of functions (in particular, of total, injective, surjective, constant, increasing and decreasing functions), without the need to resort to second-order theories. In addition, we define a minimal axiomatic system and give the completeness theorem (Henkin-style).