Jean-Yves Béziau (Classical Negation can be expressed by One of its Halves) (Béziau 1999) has given an example of a phenomenon that people consider as translation paradox. We elaborate on Béziau’s case, which concerns classical negation to the half of classical negation, as well as giving some relative background to this discussion. The translation in question turns out, not to deliver the new results but instead in the interests of illustrating the development of logic translation that widely discussed in various modern applications to computer science.
During the last decade, it has been widely shown how modal logics provide suitable tools for various theoretical formalizations in computer science. In fact, many modal systems can be found in the literature, and there are a number of areas where such logics are used. Most popular readings of the modal formula a are, for example, "0 is necessarily frue" (standard modal logic), "a will always be true" (temporal logic), "X knows fhaf a" or "X believes that a" (epistemic logic), or "after executing some program a, a will be frue" (dynamic logic), etc. In general, only one fype of modality is considered, i.e.
The modal logic S4F provides an account for the default logic of Reiter, and several modal nonmonotonic logics of knowledge and belief. In this paper we focus on a fragment of the logic S4F concerned with modal formulas called modal defaults, and on sets of modal defaults -- modal default theories. We present characterizations of S4F-expansions of modal default theories, and show that strong and uniform equivalence of modal default theories can be expressed in terms of the logical equivalence in the logic S4F. We argue that the logic S4F can be viewed as the general default logic of nested defaults. We also study special modal default theories called modal programs, and show that this fragment of the logic S4F generalizes the logic here-and-there.
Humor employs an essential false logic which masks the incongruity of two central meanings that are brought into overlap. Formalizing this false logic--if it exists, exists intersubjectively, and is indeed essential for humor--to a degree that is sufficient for computational detection and generation of humor has been a vexing problem for computational humor research. This paper will outline several such logics, in addition to the default of reasoning in a way that is one degree more implausibly than the most common-sense logic that can connect two meanings. The results are not least influenced by a pilot study asking participants to explain different types of jokes.