We define and study the problem of modular concept learning, that is, learning a concept that is a cross product of component concepts. If an element's membership in a concept depends solely on it's membership in the components, learning the concept as a whole can be reduced to learning the components. We analyze this problem with respect to different types of oracle interfaces, defining different sets of queries. If a given oracle interface cannot answer questions about the components, learning can be difficult, even when the components are easy to learn with the same type of oracle queries. While learning from superset queries is easy, learning from membership, equivalence, or subset queries is harder. However, we show that these problems become tractable when oracles are given a positive example and are allowed to ask membership queries. Keywords: Inductive Synthesis, Query-Based Learning, Modularity 1 Introduction Inductive synthesis or inductive learning is the synthesis of programs (concepts) from examples or other observations. Inductive synthesis has found application in formal methods, program analysis, software engineering, and related areas, for problems such as invariant generation (e.g.

Traditional first-order logic (FOL) reasoning systems usually rely on manual heuristics for proof guidance. We propose TRAIL: a system that learns to perform proof guidance using reinforcement learning. A key design principle of our system is that it is general enough to allow transfer to problems in different domains that do not share the same vocabulary of the training set. To do so, we developed a novel representation of the internal state of a prover in terms of clauses and inference actions, and a novel neural-based attention mechanism to learn interactions between clauses. We demonstrate that this approach enables the system to generalize from training to test data across domains with different vocabularies, suggesting that the neural architecture in TRAIL is well suited for representing and processing of logical formalisms.

A referring expression (RE) is a description that identifies a set of instances unambiguously. Mining REs from data finds applications in natural language generation, algorithmic journalism, and data maintenance. Since there may exist multiple REs for a given set of entities, it is common to focus on the most intuitive ones, i.e., the most concise and informative. In this paper we present REMI, a system that can mine intuitive REs on large RDF knowledge bases. Our experimental evaluation shows that REMI finds REs deemed intuitive by users. Moreover we show that REMI is several orders of magnitude faster than an approach based on inductive logic programming.

A coalition of agents, or a single agent, has an ethical dilemma between several statements if each joint action of the coalition forces at least one specific statement among them to be true. For example, any action in the trolley dilemma forces one specific group of people to die. In many cases, agents face ethical dilemmas because they are restricted in the amount of the resources they are ready to sacrifice to overcome the dilemma. The paper presents a sound and complete modal logical system that describes properties of dilemmas for a given limit on a sacrifice.

We present a machine-checked, formal proof of PAC learnability of the concept class of decision stumps. A formal proof has every step checked and justified using fundamental axioms of mathematics. We construct and check our proof using the Lean theorem prover. Though such a proof appears simple, a few analytic and measure-theoretic subtleties arise when carrying it out fully formally. We explain how we can cleanly separate out the parts that deal with these subtleties by using Lean features and a category theoretic construction called the Giry monad.

The Shapes Constraint Language (SHACL) has been recently introduced as a W3C recommendation to define constraints that can be validated against RDF graphs. Interactions of SHACL with other Semantic Web technologies, such as ontologies or reasoners, is a matter of ongoing research. In this paper we study the interaction of a subset of SHACL with inference rules expressed in datalog. On the one hand, SHACL constraints can be used to define a "schema" for graph datasets. On the other hand, inference rules can lead to the discovery of new facts that do not match the original schema. Given a set of SHACL constraints and a set of datalog rules, we present a method to detect which constraints could be violated by the application of the inference rules on some graph instance of the schema, and update the original schema, i.e, the set of SHACL constraints, in order to capture the new facts that can be inferred. We provide theoretical and experimental results of the various components of our approach.

Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the \emph{hardness} of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.

Theoretical computer science has been a vibrant part of computing research in India for the past 30 years. India has always had a strong mathematical tradition. One could also argue that in the 1980s and 1990s, theory offered a unique opportunity to keep up with international research in computing despite limited access to state-of-the-art hardware. The Annual International Conference Foundations of Software Technology and Theoretical Computer Science (FSTTCS) was launched in 1981. FSTTCS2 allowed Indian researchers a natural opportunity to interact with leading academics worldwide.

Programming with logic for sophisticated applications must deal with recursion and negation, which have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that support the power and ease of programming with different intended semantics. The key idea is to provide meta constraints, support the use of uncertain information in the form of either undefined values or possible combinations of values, and promote the use of knowledge units that can be instantiated by any new predicates, including predicates with additional arguments.

One person who followed up with me after my session wasn't familiar with the research area but gained an appreciation for the complexity of the problem. When we write software, even in high-level language, we are really doing all the heavy lifting to get computers to do what we want them to do. That is, as humans we still need to work at the level of the machine. Programs required an incredible amount of detail. So, it is challenging to go from high-level goals expressed in natural language, which lacks detail, to actual code.