Emerging applications are dramatically changing computer architecture requirements, with a shift toward big data that is processed using simple computations. A programmable logic-in-memory (PLiM) computer can allow memory cells to perform primitive logic operations and therefore compute without needing to communicate with a processing unit.
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.
This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about actions. Propositional Dynamic Logics (PDL's) are modal logics for describing and reasoning about system dynamics 1 in terms of properties of states and actions modeled as relations between states (see (Kozen Tiuryn 1990; Harel 1984; Parikh 1981) for surveys on PDL's, see also (Stifling 1992) for a somewhat different account). The language of PDL includes formulae built from the boolean combinations of atomic propositions that are interpreted as simple properties of states, plus the construct (R/¢, where ¢ is a formula and R is an action, whose meaning is that it is possible to perform R and terminate in a state where ¢ is true. The action R can be either an atomic action, or a complex expression denoting sequential composition, nondeterministic choice, iteration, or test. PDL's have been originally developed in Theoretical Computer Science to reason about program schemas (Fisher & Ladner 1979), and their variants have been adopted to specify and verify properties of reactive processes (e.g., Hennessy Milner Logic (Hennessy & Milner 1985; Milner 1989), modal mu-calculus (Kozen 1983; Larsen 1990; Stirling 1992)). They also of interest in Philosophical Logic as a formalism to capture "procedural reasoning" (see, for example, (Van Benthem z Bergstra 1993; Van Benthem, Van Eijck, & Stebletsova 1993; de Rijke.M 1992; Van Benthem 1991)). In Artificial Intelligence, PDL's have been extensively used in establishing decidability and computational complexity results of many formalisms: for example they have been used in investigating Common Knowledge (Halpern 1992), Conditional Logics (Friedman & Halpern 1994), Description Logics (Schild 1991; De Giacomo & Lenzerini 1994a; 1994c), Features Logics (Blackburn & Spaan 1993). However they have been only sparingly adopted for reasoning about actions, main exceptions being (Rosenschein 1991; Kautz 1980) (but also (Cohen & Levesque 1990)). 1 In this work we do not distinguish between actions and events.