ARTICLE HISTORY Compiled October 24, 2018 ABSTRACT Systems of deontic logic suffer either from being too expressive and therefore hard to mechanize, or from being too simple to capture relevant aspects of normative reasoning. In this article we look for a suitable way in between: the automation of a simple logic of normative ideality and sub-ideality that is not affected by many deontic paradoxes and that is expressive enough to capture contrary-to-duty reasoning. We show that this logic is very useful to reason on normative scenarios from which one can extract a certain kind of argumentative structure, called a Normative Detachment Structure with Ideal Conditions. The theoretical analysis of the logic is accompanied by examples of automated reasoning on a concrete legal text. Keywords: Deontic Logic - Legal Reasoning - Normative Ideality 1. Introduction In the last decades, computer systems have played an important role in assisting people in a wide range of tasks, from searching over data to decision-making, and their use is required in an increasing number of fields. One of these fields is legal reasoning. New court cases and legislations are accumulated every day. In addition, international organizations like the European Union are constantly aiming at combining and integrating separate legal systems (Burley and Walter 1993).

Synthetic Minds, which aims to build safer blockchain code, today announced it has raised $5.5 million in a new round of funding. The San Francisco startup is a graduate of the most recent summer class from the Y Combinator accelerator. The money came from Khosla Ventures and Pantera Capital (a cryptocurrency-focused fund). This funding comes on the heels of investment from Y Combinator. Synthetic Minds' core technology is called program synthesis.

In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the geometric and algebraic properties of belief functions as mathematical objects are illustrated and discussed in Part II, with a focus on both a perspective 'geometric approach' to uncertainty and an algebraic solution to the issue of conflicting evidence. In Part III we show how these theoretical developments arise from important computer vision problems (such as articulated object tracking, data association and object pose estimation) to which, in turn, the evidential formalism is able to provide interesting new solutions. Finally, some initial steps towards a generalization of the notion of total probability to belief functions are taken, in the perspective of endowing the theory of evidence with a complete battery of estimation and inference tools to the benefit of all scientists and practitioners.

Nowadays, the success of neural networks as reasoning systems is doubtless. Nonetheless, one of the drawbacks of such reasoning systems is that they work as black-boxes and the acquired knowledge is not human readable. In this paper, we present a new step in order to close the gap between connectionist and logic based reasoning systems. We show that two of the most used inference rules for obtaining negative information in rule based reasoning systems, the so-called Closed World Assumption and Negation as Finite Failure can be characterized by means of spiking neural P systems, a formal model of the third generation of neural networks born in the framework of membrane computing. Keywords: P systems, Neural-symbolic integration, Membrane computing 1. Introduction In the last years, the scientific community has paid more and more attention to artificial neural networks due to the doubtless success of such devices in many real-world problems.

This chapter discusses the institutional approach for organizing and maintaining ontologies. The theory of institutions was named and initially developed by Joseph Goguen and Rod Burstall. This theory, a metatheory based on category theory, regards ontologies as logical theories or local logics. The theory of institutions uses the category-theoretic ideas of fibrations and indexed categories to develop logical theories. Institutions unite the lattice approach of Formal Concept Analysis of Ganter and Wille with the distributed logic of Information Flow of Barwise and Seligman. The institutional approach incorporates locally the lattice of theories idea of Sowa from the theory of knowledge representation. The Information Flow Framework, which was initiated within the IEEE Standard Upper Ontology project, uses the institutional approach in its applied aspect for the comparison, semantic integration and maintenance of ontologies. This chapter explains the central ideas of the institutional approach to ontologies in a careful and detailed manner.

We briefly introduce herein a new form of distributed, multi-agent artificial intelligence, which we refer to as "tentacular." Tentacular AI is distinguished by six attributes, which among other things entail a capacity for reasoning and planning based in highly expressive calculi (logics), and which enlists subsidiary agents across distances circumscribed only by the reach of one or more given networks.

We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural variants of guardedness that allow inference to be decidable in each case, and isolate the complexity of the corresponding decision problems. Finally we show that slight changes in these conditions lead to undecidability.

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last half a century. Some examples of state-of-the-art provers are E (Schulz, 2013), VAMPIRE (Kov\'acs & Voronkov, 2013), and Prover9 (McCune, 2005-2010). Newer theorem provers, such as E, use superposition calculus in place of more traditional resolution and tableau based methods. There have also been a number of past attempts to apply machine learning methods to guiding proof search. Suttner & Ertel proposed a multilayer-perceptron based method using hand-engineered features as far back as 1990; Urban et al (2011) apply machine learning to tableau calculus; and Loos et al (2017) recently proposed a method for guiding the E theorem prover using deep nerual networks. All of this prior work, however, has one common limitation: they all rely on the axioms of classical first-order logic. Very little attention has been paid to automated theorem proving for non-classical logics. One of the only recent examples is McLaughlin & Pfenning (2008) who applied the polarized inverse method to intuitionistic propositional logic. The literature is otherwise mostly silent. This is truly unfortunate, as there are many reasons to desire non-classical proofs over classical. Constructive/intuitionistic proofs should be of particular interest to computer scientists thanks to the well-known Curry-Howard correspondence (Howard, 1980) which tells us that all terminating programs correspond to a proof in intuitionistic logic and vice versa. This work explores using Q-learning (Watkins, 1989) to inform proof search for a specific system called non-classical logic called Core Logic (Tennant, 2017).

The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack between arguments. The proposed approach is shown to satisfy some desirable properties which can not be achieved through other "naive" uses of formal languages. In particular, the approach is shown to be expressive enough to capture (besides any arbitrary finite structure) a large variety of infinite afs including two major examples from previous literature and two sample cases from the domains of multi-agent negotiation and ambient intelligence. On the computational side, we show that several decision and construction problems which are known to be polynomial time solvable in finite afs are decidable in the context of the proposed formalism and we provide the relevant algorithms. Moreover we obtain additional results concerning the case of finitary afs.

Good parameter settings are crucial to achieve high performance in many areas of artificial intelligence (AI), such as propositional satisfiability solving, AI planning, scheduling, and machine learning (in particular deep learning). Automated algorithm configuration methods have recently received much attention in the AI community since they replace tedious, irreproducible and error-prone manual parameter tuning and can lead to new state-of-the-art performance. However, practical applications of algorithm configuration are prone to several (often subtle) pitfalls in the experimental design that can render the procedure ineffective. We identify several common issues and propose best practices for avoiding them. As one possibility for automatically handling as many of these as possible, we also propose a tool called GenericWrapper4AC.