Narrow Results

We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental Schützenberger theorem. Surprisingly, the equivalence does not require any restriction to our weighted LDL. Our results hold over arbitrary (resp. totally complete) semirings for finite (resp. infinite) words. As a consequence, the equivalence problem for weighted LDL formulas over fields is decidable in doubly exponential time. In contrast to classical logics, we show that our weighted LDL is expressively incomparable to weighted LTL for finite words. We determine a fragment of the weighted LTL such that series over finite and infinite words definable by LTL formulas in this fragment are definable also by weighted LDL formulas. This is an extended version of [17].

Wide fan-in dynamic logic OR gate has always been an integral part of high speed microprocessors. However, low noise immunity of wide fan-in dynamic logic gate is always an issue of concern. For maintaining high noise immunity, various large sized PMOS keeper-based dynamic OR gates are proposed in the literature. These designs allow large leakage through them for maintaining high noise immunity which unnecessarily increases the power dissipation. This can be a critical issue for microprocessors used in battery operated devices. Independent gate (IG) FinFET devices are known to reduce leakage current through them using back gate biasing technique. In this paper, a novel FinFET-based wide fan-in dynamic OR gate has been proposed with effective leakage control and high noise immunity. This work reports a maximum leakage power reduction up to 70% while maintaining up to 90% higher noise immunity as compared to standard dynamic OR gate at low keeper size. This work also mathematically illustrates the effective leakage reduction capability of FinFET as compared to CMOS and hence proves its preference over CMOS in wide fan-in dynamic OR gate.

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

Successes of information and cognitive science brought a growing understanding that mind is based on intelligent cognitive processes, which are not limited by language and logic only. A nice overview can be found in the excellent work of Jeff Hawkins "On Intelligence." This view is that thought is a set of informational processes in the brain, and such processes have the same rationale as any other systematic informational processes. Their specifics are determined by the ways of how brain stores, structures and process this information. Systematic approach allows representing them in a diagrammatic form that can be formalized and programmed. Semiotic approach allows for the universal representation of such diagrams. In our approach, logic is just a way of synthesis of such structures, which is a small but clearly visible top of the iceberg. However, most of the efforts were traditionally put into logics without paying much attention to the rest of the mechanisms that make the entire thought system working autonomously. Dynamic fuzzy logic is reviewed and its connections with semiotics are established. Dynamic fuzzy logic extends fuzzy logic in the direction of logic-processes, which include processes of fuzzification and defuzzification as parts of logic. This extension of fuzzy logic is inspired by processes in the brain-mind. The paper reviews basic cognitive mechanisms, including instinctual drives, emotional and conceptual mechanisms, perception, cognition, language, a model of interaction between language and cognition upon the new semiotic models. The model of interacting cognition and language is organized in an approximate hierarchy of mental representations from sensory percepts at the "bottom" to objects, contexts, situations, abstract concepts-representations, and to the most general representations at the "top" of mental hierarchy. Knowledge instinct and emotions are driving feedbacks for these representations. Interactions of bottom-up and top-down processes in such hierarchical semiotic representation are essential for modeling cognition. Dynamic fuzzy logic is analyzed as a fundamental mechanism of these processes. In this paper we are trying to formalize cognitive processes of the human mind using approaches above, and provide interfaces that could allow for their practical realization in software and hardware. Future research directions are discussed.