The field of Artificial Intelligence (AI) has undoubtedly received significant attention in recent years. AI is being adopted to provide solutions to problems in fields such as medicine, engineering, education, government and several other domains. In order to analyze the state of the art of research in the field of AI, we present a systematic literature review focusing on the Evolution of AI programming languages. We followed the systematic literature review method by searching relevant databases like SCOPUS, IEEE Xplore and Google Scholar. EndNote reference manager was used to catalog the relevant extracted papers. Our search returned a total of 6565 documents, whereof 69 studies were retained. Of the 69 retained studies, 15 documents discussed LISP programming language, another 34 discussed PROLOG programming language, the remaining 20 documents were spread between Logic and Object Oriented Programming (LOOP), ARCHLOG, Epistemic Ontology Language with Constraints (EOLC), Python, C++, ADA and JAVA programming languages. This review provides information on the year of implementation, development team, capabilities, limitations and applications of each of the AI programming languages discussed. The information in this review could guide practitioners and researchers in AI to make the right choice of languages to implement their novel AI methods.

The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a tight doubly exponential bound on the model size) and hence finite satisfiability coincides with satisfiability known to be N2ExpTime-complete. Using similar constructions, we also establish 2ExpTime-completeness for finite satisfiability of the constant-free (tri)guarded fragment with transitive guards.

For a d-ary Boolean function Φ: {0, 1}d → {0, 1} and an assignment to its variables x = (x1, x2, . . . , xd) we consider the problem of finding those subsets of the variables that are sufficient to determine the function value with a given probability δ. This is motivated by the task of interpreting predictions of binary classifiers described as Boolean circuits, which can be seen as special cases of neural networks. We show that the problem of deciding whether such subsets of relevant variables of limited size k ≤ d exist is complete for the complexity class NPPP and thus, generally, unfeasible to solve. We then introduce a variant, in which it suffices to check whether a subset determines the function value with probability at least δ or at most δ − γ for 0 < γ < δ. This promise of a probability gap reduces the complexity to the class NPBPP. Finally, we show that finding the minimal set of relevant variables cannot be reasonably approximated, i.e. with an approximation factor d1−α for α > 0, by a polynomial time algorithm unless P = NP. This holds even with the promise of a probability gap.

The mathematics of quantum mechanics has been viewed and analyzed from a huge variety of different perspectives, each shedding light on different subtleties of its underlying structure and its connection to our everyday reality. Here we add an additional thread to this conceptual polyphony, demonstrating a close connection between fuzzy paraconsistent logic and quantum probabilities. This connection suggests new variations on existing interpretations of quantum reality and measurement. It also provides some tantalizing connections between the probabilistic and fuzzy logic used in modern AI systems and quantum probabilistic reasoning, which may have implications for quantum-computing implementations of logical inference based AI. The ideas here arose as a spinoff from the work reported in [Goe21], which uses a variety of paraconsistent intuitionistic logic called Constructible Duality (CD) Logic as a means for giving a rigorous logic foundation to the PLN (Probabilistic Logic Networks) logic [GIGH08] that has been used in the OpenCog AI project [GPG13a, GPG13b] for well over a decade now.

The task of Video Question Answering (VideoQA) consists in answering natural language questions about a video and serves as a proxy to evaluate the performance of a model in scene sequence understanding. Most methods designed for VideoQA up-to-date are end-to-end deep learning architectures which struggle at complex temporal and causal reasoning and provide limited transparency in reasoning steps. We present the HySTER: a Hybrid Spatio-Temporal Event Reasoner to reason over physical events in videos. Our model leverages the strength of deep learning methods to extract information from video frames with the reasoning capabilities and explainability of symbolic artificial intelligence in an answer set programming framework. We define a method based on general temporal, causal and physics rules which can be transferred across tasks. We apply our model to the CLEVRER dataset and demonstrate state-of-the-art results in question answering accuracy. This work sets the foundations for the incorporation of inductive logic programming in the field of VideoQA.

Artificial Intelligence agents are required to learn from their surroundings and to reason about the knowledge that has been learned in order to make decisions. While state-of-the-art learning from data typically uses sub-symbolic distributed representations, reasoning is normally useful at a higher level of abstraction with the use of a first-order logic language for knowledge representation. As a result, attempts at combining symbolic AI and neural computation into neural-symbolic systems have been on the increase. In this paper, we present Logic Tensor Networks (LTN), a neurosymbolic formalism and computational model that supports learning and reasoning through the introduction of a many-valued, end-to-end differentiable first-order logic called Real Logic as a representation language for deep learning. We show that LTN provides a uniform language for the specification and the computation of several AI tasks such as data clustering, multi-label classification, relational learning, query answering, semi-supervised learning, regression and embedding learning. We implement and illustrate each of the above tasks with a number of simple explanatory examples using TensorFlow 2. Keywords: Neurosymbolic AI, Deep Learning and Reasoning, Many-valued Logic.

It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic programming and concept formation. First it is shown that appropriate averaging-across-situations and renormalization of 4-valued p-bits operating in accordance with Constructible Duality (CD) logic yields PLN (Probabilistic Logic Networks) strength-and-confidence truth values. Then variations on the Curry-Howard correspondence are used to map these paraconsistent and probabilistic logics into probabilistic types suitable for use within dependent type based programming languages. Zach Weber's paraconsistent analysis of the sorites paradox is extended to form a paraconsistent / probabilistic / fuzzy analysis of concept boundaries; and a paraconsistent version of concept formation via Formal Concept Analysis is presented, building on a definition of fuzzy property-value degrees in terms of relative entropy on paraconsistent probability distributions. These general points are fleshed out via reference to the realization of probabilistic reasoning and programming and concept formation in the OpenCog AGI framework which is centered on collaborative multi-algorithm updating of a common knowledge metagraph.

Meta-Interpretive Learners, like most ILP systems, learn by searching for a correct hypothesis in the hypothesis space, the powerset of all constructible clauses. We show how this exponentially-growing search can be replaced by the construction of a Top program: the set of clauses in all correct hypotheses that is itself a correct hypothesis. We give an algorithm for Top program construction and show that it constructs a correct Top program in polynomial time and from a finite number of examples. We implement our algorithm in Prolog as the basis of a new MIL system, Louise, that constructs a Top program and then reduces it by removing redundant clauses. We compare Louise to the state-of-the-art search-based MIL system Metagol in experiments on grid world navigation, graph connectedness and grammar learning datasets and find that Louise improves on Metagol's predictive accuracy when the hypothesis space and the target theory are both large, or when the hypothesis space does not include a correct hypothesis because of "classification noise" in the form of mislabelled examples. When the hypothesis space or the target theory are small, Louise and Metagol perform equally well.

Abstract: We explore using the Suggested Upper Merged Ontology (SUMO) to develop a semantic simulation. We provide two proof-of-concept demonstrations modeling transitions in a simulated gasoline engine using a general-purpose programming language. Rather than focusing on computationally highly intensive techniques, we explore a less computationally intensive approach related to familiar software engineering testing procedures. In addition, we propose structured representations of terms based on linguistic approaches to lexicography. Keywords: Definitions, Description Logic, Model-Checking, Model-Level, Rules, Semantic Simulation, Transitionals, Truth Maintenance 1 Introduction We believe knowledge representation should be fully integrated with programming languages. Therefore, we are exploring the implementation of dynamic semantic simulations based on ontologies using a general-purpose programming language (cf., [4]). These simulations allow model-level constructs such as flows, states, transitions, microworlds, generalizations, and causation, and language features such as conditionals, threads, and looping. In this paper, we provide initial demonstrations for how the Suggested Upper Merged Ontology (SUMO) can be applied to Python-based semantic modeling. SUMO has both a rich ontology and a sophisticated inference environment built to use first-order predicate calculus [9, 15, 16, 25, 27, 28].

Abstract dialectical frameworks (ADFs) are a recently introduced powerful generalization of Dung’s popular abstract argumentation frameworks (AFs). Inspired by similar work for AFs, we introduce a decomposition scheme for ADFs, which proceeds along the ADF’s strongly connected components. We find that, for several semantics, the decomposition-based version coincides with the original semantics, whereas for others, it gives rise to a new semantics. These new semantics allow us to deal with pertinent problems such as odd-length negative cycles in a more general setting, that for instance also encompasses logic programs. We perform an exhaustive analysis of the computational complexity of these new, so-called naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore, in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.