Toward a probability theory for product logic: states, integral representation and reasoning

The aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure. Furthermore, the relation between states and measures is shown to be one-one. In addition, we study geometrical properties of the convex set of states and show that extremal states, i.e., the extremal points of the state space, are the same as the truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal logic for probabilistic reasoning on product logic events and prove soundness and completeness with respect to probabilistic spaces, where the algebra is a free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur

Predictive intelligence to the edge through approximate collaborative context reasoning

We focus on Internet of Things (IoT) environments where a network of sensing and computing devices are responsible to locally process contextual data, reason and collaboratively infer the appearance of a specific phenomenon (event). Pushing processing and knowledge inference to the edge of the IoT network allows the complexity of the event reasoning process to be distributed into many manageable pieces and to be physically located at the source of the contextual information. This enables a huge amount of rich data streams to be processed in real time that would be prohibitively complex and costly to deliver on a traditional centralized Cloud system. We propose a lightweight, energy-efficient, distributed, adaptive, multiple-context perspective event reasoning model under uncertainty on each IoT device (sensor/actuator). Each device senses and processes context data and infers events based on different local context perspectives: (i) expert knowledge on event representation, (ii) outliers inference, and (iii) deviation from locally predicted context. Such novel approximate reasoning paradigm is achieved through a contextualized, collaborative belief-driven clustering process, where clusters of devices are formed according to their belief on the presence of events. Our distributed and federated intelligence model efficiently identifies any localized abnormality on the contextual data in light of event reasoning through aggregating local degrees of belief, updates, and adjusts its knowledge to contextual data outliers and novelty detection. We provide comprehensive experimental and comparison assessment of our model over real contextual data with other localized and centralized event detection models and show the benefits stemmed from its adoption by achieving up to three orders of magnitude less energy consumption and high quality of inference

Distributed localized contextual event reasoning under uncertainty

We focus on Internet of Things (IoT) environments where sensing and computing devices (nodes) are responsible to observe, reason, report and react to a specific phenomenon. Each node captures context from data streams and reasons on the presence of an event. We propose a distributed predictive analytics scheme for localized context reasoning under uncertainty. Such reasoning is achieved through a contextualized, knowledge-driven clustering process, where the clusters of nodes are formed according to their belief on the presence of the phenomenon. Each cluster enhances its localized opinion about the presence of an event through consensus realized under the principles of Fuzzy Logic (FL). The proposed FLdriven consensus process is further enhanced with semantics adopting Type-2 Fuzzy Sets to handle the uncertainty related to the identification of an event. We provide a comprehensive experimental evaluation and comparison assessment with other schemes over real data and report on the benefits stemmed from its adoption in IoT environments

Arguments Whose Strength Depends on Continuous Variation

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so that ignorance of their nature is profound