We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows to aggregate weights of tuples, compare such aggregates, and use them to build more complex formulas. We provide locality properties of fragments of this logic including Feferman-Vaught decompositions and a Gaifman normal form for a fragment called FOW1, as well as a localisation theorem for a larger fragment called FOWA1. This fragment can express concepts from various machine learning scenarios. Using the locality properties, we show that concepts definable in FOWA1 over a weighted background structure of at most polylogarithmic degree are agnostically PAC-learnable in polylogarithmic time after pseudo-linear time preprocessing.

Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf. We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.

The gossip problem is described by Hedetniemi et al. in their survey [10] as follows: Gossiping refers to the information dissemination problem that exists when each member of a set A of n individuals knows a unique piece of information and must transmit it to every other person. The problem is solved by producing a sequence of unordered pairs (i, j), i, j A, each of which represents a phone call made between a pair of individuals, such that during each call the two people involved exchange all of the information they know at that time; and such that at the end of the sequence of calls, everybody knows everything. Such a calling sequence, which completes gossiping among the n people, is called complete. The gossip problem has been studied by many researchers, in particular, in the context of communication networks. While the most widely studied variant is the following optimization problem: M Minimize the number of calls in a complete calling sequence.

The problem we want to solve is how to generate all theorems of a given size in the implicational fragment of propositional intuitionistic linear logic. We start by filtering for linearity the proof terms associated by our Prolog-based theorem prover for Implicational Intuitionistic Logic. This works, but using for each formula a PSPACE-complete algorithm limits it to very small formulas. We take a few walks back and forth over the bridge between proof terms and theorems, provided by the Curry-Howard isomorphism, and derive step-by-step an efficient algorithm requiring a low polynomial effort per generated theorem. The resulting Prolog program runs in O(N) space for terms of size N and generates in a few hours 7,566,084,686 theorems in the implicational fragment of Linear Intuitionistic Logic together with their proof terms in normal form. As applications, we generate datasets for correctness and scalability testing of linear logic theorem provers and training data for neural networks working on theorem proving challenges. The results in the paper, organized as a literate Prolog program, are fully replicable. Keywords: combinatorial generation of provable formulas of a given size, intuitionistic and linear logic theorem provers, theorems of the implicational fragment of propositional linear intuitionistic logic, Curry-Howard isomorphism, efficient generation of linear lambda terms in normal form, Prolog programs for lambda term generation and theorem proving.

Understanding the meaning of a text is a fundamental challenge of natural language understanding (NLU) and from its early days, it has received significant attention through question answering (QA) tasks. We introduce a general semantics-based framework for natural language QA and also describe the SQuARE system, an application of this framework. The framework is based on the denotational semantics approach widely used in programming language research. In our framework, valuation function maps syntax tree of the text to its commonsense meaning represented using basic knowledge primitives (the semantic algebra) coded using answer set programming (ASP). We illustrate an application of this framework by using VerbNet primitives as our semantic algebra and a novel algorithm based on partial tree matching that generates an answer set program that represents the knowledge in the text. A question posed against that text is converted into an ASP query using the same framework and executed using the s(CASP) goal-directed ASP system. Our approach is based purely on (commonsense) reasoning. SQuARE achieves 100% accuracy on all the five datasets of bAbI QA tasks that we have tested. The significance of our work is that, unlike other machine learning based approaches, ours is based on "understanding" the text and does not require any training. SQuARE can also generate an explanation for an answer while maintaining high accuracy.

The requirement for artificial intelligence (AI) to provide explanations in making critical decision becomes increasingly important due to concerns of accountability, trust, as well as ethics. Such an explainable AI is expected to be capable of providing justifications that are human-understandable. A form of reasoning for providing explanations to an observation, known as abduction, has been well studied in AI, particularly in knowledge representation and reasoning. It extends to logic programming, dubbed abductive logic programming [3], and it has a wide variety of usage, e.g., in planning, scheduling, reasoning of rational agents, security protocols verification, biological systems, and machine ethics.

Answer set programming is a leading declarative constraint programming paradigm with wide use for complex knowledge-intensive applications. Modern answer set programming languages support many equivalent ways to model constraints and specifications in a program. However, so far answer set programming has failed to develop systematic methodologies for building representations that would uniformly lend well to automated processing. This suggests that encoding selection, in the same way as algorithm selection and portfolio solving, may be a viable direction for improving performance of answer-set solving. The necessary precondition is automating the process of generating possible alternative encodings. Here we present an automated rewriting system, the Automated Aggregator or AAgg, that given a non-ground logic program, produces a family of equivalent programs with complementary performance when run under modern answer set programming solvers. We demonstrate this behavior through experimental analysis and propose the system's use in automated answer set programming solver selection tools.

Hybrid Answer Set Programming (Hybrid ASP) is an extension of Answer Set Programming (ASP) that allows ASPlike rules to interact with outside sources. The Splitting Set Theorem is an important and extensively used result for ASP. The paper introduces the Splitting Set Theorem for Hybrid ASP, which is for Hybrid ASP the equivalent of the Splitting Set Theorem, and shows how it can be applied to simplify computing answer sets for Hybrid ASP programs most relevant for practical applications. An important result for logic programs is the Splitting Set Theorem [12], which shows how computing an answer set for a program can be broken into several tasks of the same kind for smaller programs. The theorem and its more general variant the Splitting Sequence Theorem are extensively used for proving other theorems, for instance in [1], [9] or [3] among many others. Hybrid Answer Set Programming (Hybrid ASP) [4] is an extension of ASP that allows ASPlike rules to interact with outside sources, which makes Hybrid ASP well suited for practical applications.

We study a dynamic version of multi-agent path finding problem (called D-MAPF) where existing agents may leave and new agents may join the team at different times. We introduce a new method to solve D-MAPF based on conflict-resolution. The idea is, when a set of new agents joins the team and there are conflicts, instead of replanning for the whole team, to replan only for a minimal subset of agents whose plans conflict with each other. We utilize answer set programming as part of our method for planning, replanning and identifying minimal set of conflicts.

Autonomous Intelligent Systems are designed to reduce the need for human intervention in our daily life. However, the full benefit of these new systems will be attained only if they are aligned with society's values and ethical principles. Adopting ethical approaches to building such systems has been attracting a lot of attention in the recent years. The global concern about the ethical behavior of this kind of technologies has manifested in many initiatives at different levels. As examples, we mention: the IEEE initiative for ethically aligned design of autonomous intelligent systems ('Ethics in Action'