Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints `a la IFF, possibly annotated with a probability value. We first present the overall abductive language, and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.

We introduce a novel logic-based system for reasoning over data streams, which relies on a framework enabling a tight, fine-tuned interaction between Apache Flink and the I^2-DLV system. The architecture allows to take advantage from both the powerful distributed stream processing capabilities of Flink and the incremental reasoning capabilities of I^2-DLV based on overgrounding techniques. Besides the system architecture, we illustrate the supported input language and its modeling capabilities, and discuss the results of an experimental activity aimed at assessing the viability of the approach. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property.

Each year, PhD students from around the world apply for the Facebook Fellowship, a program designed to encourage and support promising doctoral students who are engaged in innovative and relevant research in areas related to computer science and engineering. Fellowship recipients receive tuition funding for up to two years to conduct their research at their respective universities, independently of Facebook. To learn about award details, eligibility, and more, visit the program page below. Xinyun is a PhD student at UC Berkeley working with Professor Dawn Song and is expected to graduate in 2022. Her research explores the intersection of deep learning, programming languages, and security, focused on neural program synthesis and adversarial machine learning (ML).

Symbolic knowledge can provide crucial inductive bias for training neural models, especially in low data regimes. A successful strategy for incorporating such knowledge involves relaxing logical statements into sub-differentiable losses for optimization. In this paper, we study the question of how best to relax logical expressions that represent labeled examples and knowledge about a problem; we focus on sub-differentiable t-norm relaxations of logic. We present theoretical and empirical criteria for characterizing which relaxation would perform best in various scenarios. In our theoretical study driven by the goal of preserving tautologies, the Lukasiewicz t-norm performs best. However, in our empirical analysis on the text chunking and digit recognition tasks, the product t-norm achieves best predictive performance. We analyze this apparent discrepancy, and conclude with a list of best practices for defining loss functions via logic.

In Proc. of the 2016 Conf. on Embedded Real Time Softw. and Systems.

An epistemic model for decentralized discrete-event systems with non-binary control is presented. This framework combines existing work on conditional control decisions with existing work on formal reasoning about knowledge in discrete-event systems. The novelty in the model presented is that the necessary and sufficient conditions for problem solvability encapsulate the actions that supervisors must take. This direct coupling between knowledge and action -- in a formalism that mimics natural language -- makes it easier, when the problem conditions fail, to determine how the problem requirements should be revised.

To design and engineer ethical and legal reasoners and responsible systems, Benzm\"{u}ller, Parent and van der Torre introduce LogiKEy methodology based on the semantical embedding of deontic logics into classic higher-order logic. In this paper, we considerably extend the LogiKEy deontic logics and dataset using an algebraic approach. We develop theory of input/output operations for normative reasoning on top of Boolean algebras.

If an agent, or a coalition of agents, has a strategy, knows that she has a strategy, and knows what the strategy is, then she has a know-how strategy. Several modal logics of coalition power for know-how strategies have been studied before. The contribution of the article is three-fold. First, it proposes a new class of know-how strategies that depend on the intelligence information about the opponents' actions. Second, it shows that the coalition power modality for the proposed new class of strategies cannot be expressed through the standard know-how modality. Third, it gives a sound and complete logical system that describes the interplay between the coalition power modality with intelligence and the distributed knowledge modality in games with imperfect information.

We approach the question "What is Consciousness?" in a new way, not as Descartes' "systematic doubt", but as how organisms find their way in their world. Finding one's way involves finding possible uses of features of the world that might be beneficial or avoiding those that might be harmful. "Possible uses of X to accomplish Y" are "Affordances". The number of uses of X is indefinite (or unknown), the different uses are unordered and are not deducible from one another. All biological adaptations are either affordances seized by heritable variation and selection or, far faster, by the organism acting in its world finding uses of X to accomplish Y. Based on this, we reach rather astonishing conclusions: (1) Artificial General Intelligence based on Universal Turing Machines (UTMs) is not possible, since UTMs cannot "find" novel affordances. (2) Brain-mind is not purely classical physics for no classical physics system can be an analogue computer whose dynamical behavior can be isomorphic to "possible uses". (3) Brain mind must be partly quantum - supported by increasing evidence at 6.0 sigma to 7.3 Sigma. (4) Based on Heisenberg's interpretation of the quantum state as "Potentia" converted to "Actuals" by Measurement, a natural hypothesis is that mind actualizes Potentia. This is supported at 5.2 Sigma. Then Mind's actualizations of entangled brain-mind-world states are experienced as qualia and allow "seeing" or "perceiving" of uses of X to accomplish Y. We can and do jury-rig. Computers cannot. (5) Beyond familiar quantum computers, we discuss the potentialities of Trans-Turing-Systems.