An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic reasoning and predicative symbolic reasoning over data. We return to the era of reasoning with a full joint distribution before the advent of Bayesian networks. We then discuss that a full joint distribution over models of exponential size in propositional logic and of infinite size in predicate logic should be simply derived from a full joint distribution over data of linear size. We show that the same process is not only enough to generalise the logical consequence relation of predicate logic but also to provide a new perspective to rethink well-known limitations such as the undecidability of predicate logic, the symbol grounding problem and the principle of explosion. The reproducibility of this theoretical work is fully demonstrated by the included proofs.

Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel data structures, we propose sequence-heap separation logic which integrates sequences into logical reasoning on heap-manipulated programs. Quantifiers over sequence variables and singleton heap storing sequence (sequence singleton heap) are new members in our logic. Further, we study the satisfiability problem of two fragments. The propositional fragment of sequence-heap separation logic is decidable, and the fragment with 2 alternations on program variables and 1 alternation on sequence variables is undecidable. In addition, we explore boundaries between decidable and undecidable fragments of the logic with prenex normal form.

This paper presents Non-Axiomatic Term Logic (NATL) as a theoretical computational framework of humanlike symbolic reasoning in artificial intelligence. NATL unites a discrete syntactic system inspired from Aristotle's term logic and a continuous semantic system based on the modern idea of distributed representations, or embeddings. This paper positions the proposed approach in the phylogeny and the literature of logic, and explains the framework. As it is yet no more than a theory and it requires much further elaboration to implement it, no quantitative evaluation is presented. Instead, qualitative analyses of arguments using NATL, some applications to possible cognitive science/robotics-related research, and remaining issues towards a machinery implementation are discussed.

A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that enables reasoning with defeasible rules is presented. Finally, reasoning by cases using an argumentation tableau is discussed.

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original inconsistent instance. It has been shown before that database repairs can be specified as the stable models of a disjunctive logic program. In this paper we show how to use the repair programs to transform the problem of consistent query answering into a problem of reasoning w.r.t. a theory written in second-order predicate logic. It also investigated how a first-order theory can be obtained instead by applying second-order quantifier elimination techniques.

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.

To talk about Reasoning, it's important to understand how we got here. This article covers what I call the pre-history of Classical AI -- those parts of the story that happened before the invention of modern computers (pre 1950s) but are crucial to understanding why we believe that AI is possible. This is part 2 in a series on Reasoning. Like most things, the very beginnings of classical AI is rooted in philosophy, and starts in the ancient world (the Greeks, Indians, and Chinese all had some early forms of logic). But, as I'm not a masochist we start in more contemporary times with two big ideas that lay the foundation for modern AI: The development of logic was humanity's first great attempt at mechanizing intelligence, and the basis for modern logic lies with George Boole, Charles Pierce, and Gottlob Frege.

Predicate logic in which predicates take only individuals as arguments and quantifiers only bind individual variables. Predicate logic in which predicates take other predicates as arguments and quantifiers bind predicate variables. For example, second-order predicates take first-order predicates as arguments. Order n predicates take order n-1 predicates as arguments (n 1). Predicate logic that does not exclude interpretations with empty domains.

Names only appear which are in no sense bibliographic references; otherwise they are to be found in the author index.]

This paper provides a gentle introduction to problem solving with the IDP3 system. The core of IDP3 is a finite model generator that supports first order logic enriched with types, inductive definitions, aggregates and partial functions. It offers its users a modeling language that is a slight extension of predicate logic and allows them to solve a wide range of search problems. Apart from a small introductory example, applications are selected from problems that arose within machine learning and data mining research. These research areas have recently shown a strong interest in declarative modeling and constraint solving as opposed to algorithmic approaches. The paper illustrates that the IDP3 system can be a valuable tool for researchers with such an interest. The first problem is in the domain of stemmatology, a domain of philology concerned with the relationship between surviving variant versions of text. The second problem is about a somewhat related problem within biology where phylogenetic trees are used to represent the evolution of species. The third and final problem concerns the classical problem of learning a minimal automaton consistent with a given set of strings. For this last problem, we show that the performance of our solution comes very close to that of a state-of-the art solution. For each of these applications, we analyze the problem, illustrate the development of a logic-based model and explore how alternatives can affect the performance.