Doxastic logic: a new approach

Abstract

In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The systems in this paper can be used to symbolise not only the doxastic states of perfectly rational individuals, but also the beliefs of finite humans (and human-like agents). Proof-theoretically, I will use a tableau technique. Every system is combined with predicate logic with necessary identity and 'possibilist' quantifiers and modal logic with two kinds of modal operators for relative and absolute necessity. The semantics is a possible world semantics. Finally, I prove that every tableau system in the paper is sound and complete with respect to its semantics.

Quantified Temporal Alethic Boulesic Doxastic Logic

“…The results in this paper build on the author's previous work on (non-temporal) doxastic logic[89] and (non-temporal) boulesic logic[91]. See also[88,90].…”

“…The conditions in Table 4 are concerned with some possible restrictions on the doxastic accessibility relation ('d' stands for 'doxastic'). In standard doxastic logic, the doxastic accessibility relation is usually treated as a 2-place relation (see, for example [33,76]; however, see also [37,89]). In this paper, D is a 4-place relation.…”

“…I focus on the concept of belief in this paper. For reasons why this approach to doxastic logic is attractive, see [89].…”

Árboles semánticos para algunas lógicas alético-epistémico-doxásticas

“…S5 2 es la lógica más fuerte de todas. Al tener no sólo a (52), sino también a (42), al que llega sólo en conjunción con (T2), S5 2 ha sido vista por algunos lógicos como el sistema que defiende que todas las propiedades modales son necesarias (cualquier sistema con (42) sólo acepta que lo son las propiedades necesarias) [16, pp. 49-50].…”

“…Hay sistemas lógicos que no consiguen forzar el actualismo. En la última década, Daniel Rönnedal ha desarrollado varios sistemas multimodales [39,40,41,42], pero su sistema más ambicioso [43] es una fusión que es doxástica, alética, temporal, volitiva (boulesic) y con cuantificadores de primer orden. En estos sistemas, los mundos aléticos, doxásticos y volitivos sólo se distinguen por las relaciones en las que se encuentran.…”