We study the problem of inducing logic programs in a probabilistic setting, in which both the example descriptions and their classification can be probabilistic. The setting is incorporated in the probabilistic rule learner ProbFOIL+, which combines principles of the rule learner FOIL with ProbLog, a probabilistic Prolog. We illustrate the approach by applying it to the knowledge base of NELL, the Never-Ending Language Learner.

Compositionality is a fundamental notion in computation whereby complex abstractions can be constructed from simpler ones, but this property has so far escaped the paradigm of end-user programming from examples or natural language. Existing approaches restrict end users to only give holistic end-to-end specifications, which limits the expressivity and scalability of these approaches to relatively simple programs in very restricted domains. In this paper we propose a new approach to end-user program synthesis in which input can be given in a compositional manner through a combination of natural language and examples. We present a domain-agnostic program synthesis algorithm and demonstrate its application to an expressive string manipulation language. We evaluate on a range of complex examples from help forums that are beyond the scope of previous systems.

In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Recently, Fang and Liu extended the situation calculus to account for multi-agent knowledge and belief change. In this paper, based on their framework, we investigate progression of both belief and knowledge in the single-agent propositional case. We first present a model-theoretic definition of progression of knowledge and belief. We show that for propositional actions, i.e., actions whose precondition axioms and successor state axioms are propositional formulas, progression of knowledge and belief reduces to forgetting in the logic of knowledge and belief, which we show is closed under forgetting. Consequently, we are able to show that for propositional actions, progression of knowledge and belief is always definable in the logic of knowledge and belief.

In this paper we investigate situation calculus action theories extended with ontologies, expressed as description logics TBoxes that act as state constraints. We show that this combination, while natural and desirable, is particularly problematic: it leads to undecidability of the simplest form of reasoning, namely satisfiability, even for the simplest kinds of description logics and the simplest kind of situation calculus action theories.

Knowledge and Action Bases (KABs) have been put forward as a semantically rich representation of a domain, using a DL KB to account for its static aspects, and actions to evolve its extensional part over time, possibly introducing new objects. Recently, KABs have been extended to manage inconsistency, with ad-hoc verification techniques geared towards specific semantics. This work provides a twofold contribution along this line of research. On the one hand, we enrich KABs with a high-level, compact action language inspired by Golog, obtaining so called Golog-KABs (GKABs). On the other hand, we introduce a parametric execution semantics for GKABs, so as to elegantly accomodate a plethora of inconsistency-aware semantics based on the notion of repair. We then provide several reductions for the verification of sophisticated first-order temporal properties over inconsistency-aware GKABs, and show that it can be addressed using known techniques, developed for standard KABs.

Large formal mathematical knowledge bases encode considerable parts of advanced mathematics and exact science, allowing deep semantic computer assistance and verification of complicated theories down to the atomic logical rules. An essential part of automated reasoning over such large theories are methods learning selection of relevant knowledge from the thousands of proofs in the corpora. Such methods in turn rely on efficiently computable features characterizing the highly structured and inter-related mathematical statements.  In this work we (i) propose novel semantic features characterizing the statements in such large semantic knowledge bases, (ii) propose and carry out their efficient implementation using deductive-AI data-structures such as substitution trees and discrimination nets, and (iii) show that they significantly improve the strength of existing knowledge selection methods and automated reasoning methods over the large formal knowledge bases. In particular, on a standard large-theory benchmark we improve the average predicted rank of a mathematical statement needed for a proof by 22% in comparison with state of the art. This allows us to prove 8% more theorems in comparison with state of the art.

Existential rules (also known as Datalog+/- or tuple-generating dependencies) have been intensively studied in recent years as a prominent formalism in knowledge representation and database systems. We consider them here as a querying formalism, extending classical Datalog, the language of deductive databases. It is well known that the classes of databases recognized by (Boolean) existential rule queries are closed under homomorphisms. Also, due to the existence of a semi-decision procedure (the chase), these database classes are recursively enumerable. We show that, conversely, every homomorphism-closed recursively enumerable query can be expressed as an existential rule query, thus arriving at a precise characterization of existential rules by model-theoretic and computational properties. Although the result is very intuitive, the proof turns out to be non-trivial. This result can be seen as a very expressive counterpart of the prominent Lyndon-Los-Tarski-Theorem characterizing the homomorphism-closed fragment of first-order logic. Notably, our result does not presume the existence of any additional built-in structure on the queried data, such as a linear order on the domain, which is a typical requirement for other characterizations in the spirit of descriptive complexity.

Geometry reasoning and proof form a major and challenging component in the K-121 mathematics curriculum. Although several computerized systems exist that help students learn and practice general geometry concepts, they do not target geometry proof problems, which are more advanced and difficult. Powerful geometry theorem provers also exist, however they typically employ advanced algebraic methods and generate complex, difficult to understand proofs, and thus do not meet general K-12 students’ educational needs. This paper tackles these weaknesses of prior systems by introducing a geometry proof system, iGeoTutor, capable of generating human-readable elementary proofs, i.e. proofs using standard Euclidean axioms. We have gathered 77 problems in total from various sources, including ones unsolvable by other systems and from Math competitions. iGeoTutor solves all but two problems in under two minutes each, and more importantly, demonstrates a much more effective and intelligent proof search than prior systems. We have also conducted a pilot study with 12 high school students, and the results show that iGeoTutor provides a clear benefit in helping students learn geometry proofs. We are in active discussions with Khan Academy and local high schools for possible adoption of iGeo-Tutor in real learning environments.

General Game Playing aims to create AI systems that can understand the rules of new games and learn to play them effectively without human intervention. The recent proposal for general game-playing robots extends this to AI systems that play games in the real world. Execution monitoring becomes a necessity when moving from a virtual to a physical environment, because in reality actions may not be executed properly and (human) opponents may make illegal game moves. We develop a formal framework for execution monitoring by which an action theory that provides an axiomatic description of a game is automatically embedded in a meta-game for a robotic player — called the arbiter — whose role is to monitor and correct failed actions. This allows for the seamless encoding of recovery behaviours within a meta-game, enabling a robot to recover from these unexpected events.

This paper relates two extensively studied formalisms: abstract dialectical frameworks and logic programs with generalized atoms or similar constructs. While the syntactic similarity is easy to see, also a strong relation between various stable model semantics proposed for these formalisms is shown by means of a unifying framework in which these semantics are restated in terms of program reducts and an immediate consequence operator, where program reducts have only minimal differences. This approach has advantages for both formalisms, as for example implemented systems for one formalism are usable for the other, and properties such as computational complexity do not have to be rediscovered. As a first, concrete result of this kind, one stable model semantics based on program reducts and subset-minimality that reached a reasonable consensus for logic programs with generalized atoms provides a novel, alternative semantics for abstract dialectical frameworks.