In complex areas such as law and science, knowledge has been in centuries formulated by primarily describing prototypical instances and properties, and then by overriding the general theory to include possible exceptions. For example, many laws are formulated by adding new norms that, in case of conflicts, may partially or completely override the previous ones. Similarly, biologists have been incrementally introducing exceptions to general properties. For instance, the human heart is usually located in the left-hand half of the thorax. Still there are exceptional individuals, with so-called situs inversus, whose heart is located on the opposite side. Eukariotic cells are those with a proper nucleus, by definition. Still they comprise mammalian red blood cells, that in their mature stage have no nucleus.

This note is a sketch of how the concept of robopsychology and robophilosophy could be reinterpreted and repositioned in the spirit of the original vocation of psychology and philosophy. The notion of the robopsychology as a fictional science and a fictional occupation was introduced by Asimov in the middle of the last century. The robophilosophy, on the other hand, is only a few years old today. But at this moment, none of these new emerging disciplines focus on the fundamental and overall issues of the development of artificial general intelligence. Instead, they focus only on issues that, although are extremely important, play a complementary role, such as moral or ethical ones, rather than the big questions of life. We try to outline a conception in which the robophilosophy and robopsychology will be able to play a similar leading rule in the progress of artificial intelligence than the philosophy and psychology have done in the progress of human intelligence. To facilitate this, we outline the idea of a visual artificial language and interactive theorem prover-based computer application called Prime Convo Assistant. The question to be decided in the future is whether we can develop such an application. And if so, can we build a computer game on it, or even an esport game? It may be an interesting question in order for this game will be able to transform human thinking on the widest possible social scale and will be able to develop a standard mathematical logic-based communication channel between human and machine intelligence.

It is NPcomplete even in one of the simplest cases: propositional definite Horn [Lib20a]. A way to forget variables from a definite Horn formula is to recursively replace them [Lib20a]. Forgetting from general Horn formulae can be done by turning the formula definite Horn before forgetting and adding some clauses afterwards [Lib20a]. Therefore, while this article concentrates on definite Horn formulae, the results apply to the general Horn case. In particular, it shows how efficiency increases by modifying the input formula before running the replacement algorithm.

Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, an original framework with mixed sets defined as function images of symbol type domains is first proposed. Syntax and semantics are explicitly distinguished. Then, both continuous (interval) and discrete (signed, boolean) symbol types are used to model dependencies through linear and polynomial functions, so leading to mixed zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes with typed symbols. Polynotopes can both propagate a mixed encoding of intervals and describe the behavior of logic gates. A functional completeness result is given, as well as an inclusion method for elementary nonlinear and switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a stochastic uncertainty paradigm are outlined. Finally, several discrete, continuous and hybrid numerical examples including comparisons illustrate the effectiveness of the theoretical results.

We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). We focus on recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL, but performs a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). We obtain a proper extension of the stable models semantics for the general case of arbitrary temporal formulas. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between infinite and finite traces. We also provide other useful results, such as the translation into other formalisms like Quantified Equilibrium Logic or Second-order LTL, and some techniques for computing temporal stable models based on automata. In a second part, we focus on practical aspects, defining a syntactic fragment called temporal logic programs closer to ASP, and explain how this has been exploited in the construction of the solver TELINGO.

Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence, non-classical reasoning approaches are required. Here, we investigate probabilistic epistemic argumentation as a tool for automated reasoning about legal cases. We introduce a general scheme to model legal cases as probabilistic epistemic argumentation problems, explain how evidence can be modeled and sketch how explanations for legal decisions can be generated automatically. Our framework is easily interpretable, can deal with cyclic structures and imprecise probabilities and guarantees polynomial-time probabilistic reasoning in the worst-case.

Describing complex objects as the composition of elementary ones is a common strategy in computer science and science in general. This paper contributes to the foundations of knowledge representation and database theory by introducing and studying the sequential composition of propositional Horn theories. Specifically, we show that the notion of composition gives rise to a family of monoids and near-semirings, which we will call {\em Horn monoids} and {\em Horn near-semirings} in this paper. Particularly, we show that the combination of sequential composition and union yields the structure of a finite idempotent near-semiring. We also show that the restricted class of proper propositional Krom-Horn theories, which only contain rules with exactly one body atom, yields a finite idempotent semiring. On the semantic side, we show that the immediate consequence or van Emden-Kowalski operator of a theory can be represented via composition, which allows us to compute its least model semantics without any explicit reference to operators. This bridges the conceptual gap between the syntax and semantics of a propositional Horn theory in a mathematically satisfactory way. Moreover, it gives rise to an algebraic meta-calculus for propositional Horn theories. In a broader sense, this paper is a first step towards an algebra of rule-based logical theories and in the future we plan to adapt and generalize the methods of this paper to wider classes of theories, most importantly to first-, and higher-order logic programs, and non-monotonic logic programs under the stable model or answer set semantics and extensions thereof.

This glossary of artificial intelligence is a list of definitions of terms and concepts relevant to the study of artificial intelligence, its sub-disciplines, and related fields. Related glossaries include Glossary of computer science, Glossary of robotics, and Glossary of machine vision. Also stochastic Hopfield network with hidden units. Also exhaustive search or generate and test. Also deep structured learning or hierarchical learning.

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs, experimental evaluations are limited to only a few programs. Existing methods to generate random logic programs are limited to propositional programs and often impose stringent syntactic restrictions. We present a novel approach to generating random logic programs and random probabilistic logic programs using constraint programming, introducing a new constraint to control the independence structure of the underlying probability distribution. We also provide a combinatorial argument for the correctness of the model, show how the model scales with parameter values, and use the model to compare probabilistic inference algorithms across a range of synthetic problems. Our model allows inference algorithm developers to evaluate and compare the algorithms across a wide range of instances, providing a detailed picture of their (comparative) strengths and weaknesses.

Given the recent successes of Deep Learning in AI there has been increased interest in the role and need for explanations in machine learned theories. A distinct notion in this context is that of Michie's definition of Ultra-Strong Machine Learning (USML). USML is demonstrated by a measurable increase in human performance of a task following provision to the human of a symbolic machine learned theory for task performance. A recent paper demonstrates the beneficial effect of a machine learned logic theory for a classification task, yet no existing work has examined the potential harmfulness of machine's involvement in human learning. This paper investigates the explanatory effects of a machine learned theory in the context of simple two person games and proposes a framework for identifying the harmfulness of machine explanations based on the Cognitive Science literature. The approach involves a cognitive window consisting of two quantifiable bounds and it is supported by empirical evidence collected from human trials. Our quantitative and qualitative results indicate that human learning aided by a symbolic machine learned theory which satisfies a cognitive window has achieved significantly higher performance than human self learning. Results also demonstrate that human learning aided by a symbolic machine learned theory that fails to satisfy this window leads to significantly worse performance than unaided human learning.