Many procedures for SA T -related problems, in particular for those requiring the complete enumeration of satisfying truth assignments, rely their efficiency and effectiveness on the detection of (possibly small) partial assignments satisfying an input formula. Surprisingly, there seems to be no unique universally-agreed definition of formula satisfaction by a partial assignment in the literature. In this paper we analyze in deep the issue of satisfaction by partial assignments, raising a flag about some ambiguities and subtleties of this concept, and investigating their practical consequences. We identify two alternative notions that are implicitly used in the literature, namely verification and entailment, which coincide if applied to CNF formulas but differ and present complementary properties if applied to non-CNF or to existentially-quantified formulas. We show that, although the former is easier to check and as such is implicitly used by most current search procedures, the latter has better theoretical properties, and can improve the efficiency and effectiveness of enumeration procedures. 1 Introduction Motivations.

The tree-width of a multivariate polynomial is the tree-width of the hypergraph with hyperedges corresponding to its terms. Multivariate polynomials of bounded tree-width have been studied by Makowsky and Meer as a new sparsity condition that allows for polynomial solvability of problems which are intractable in general. We consider a variation on this theme for Boolean variables. A representation of a Boolean function as the sign of a polynomial is called a polynomial threshold representation. We discuss Boolean functions representable as polynomial threshold functions of bounded tree-width and present two applications to Bayesian network classifiers, a probabilistic graphical model. Both applications are in Explainable Artificial Intelligence (XAI), the research area dealing with the black-box nature of many recent machine learning models. We also give a separation result between the representational power of positive and general polynomial threshold functions.

In many settings, there is an organizer who would like to divide a set of agents into $k$ coalitions, and cares about the friendships within each coalition. Specifically, the organizer might want to maximize utilitarian social welfare, maximize egalitarian social welfare, or simply guarantee that every agent will have at least one friend within his coalition. However, in many situations, the organizer is not familiar with the friendship connections, and he needs to obtain them from the agents. In this setting, a manipulative agent may falsely report friendship connections in order to increase his utility. In this paper, we analyze the complexity of finding manipulation in such $k$-coalitional games on graphs. We also introduce a new type of manipulation, socially-aware manipulation, in which the manipulator would like to increase his utility without decreasing the social welfare. We then study the complexity of finding socially-aware manipulation in our setting. Finally, we examine the frequency of socially-aware manipulation and the running time of our algorithms via simulation results.

Decision diagrams (DDs) are powerful tools to represent effectively propositional formulas, which are largely used in many domains, in particular in formal verification and in knowledge compilation. Some forms of DDs (e.g., OBDDs, SDDs) are canonical, that is, (under given conditions on the atom list) they univocally represent equivalence classes of formulas. Given the limited expressiveness of propositional logic, a few attempts to leverage DDs to SMT level have been presented in the literature. Unfortunately, these techniques still suffer from some limitations: most procedures are theory-specific; some produce theory DDs (T-DDs) which do not univocally represent T-valid formulas or T-inconsistent formulas; none of these techniques provably produces theory-canonical T-DDs, which (under given conditions on the T-atom list) univocally represent T-equivalence classes of formulas. Also, these procedures are not easy to implement, and very few implementations are actually available. In this paper, we present a novel very-general technique to leverage DDs to SMT level, which has several advantages: it is very easy to implement on top of an AllSMT solver and a DD package, which are used as blackboxes; it works for every form of DDs and every theory, or combination thereof, supported by the AllSMT solver; it produces theory-canonical T-DDs if the propositional DD is canonical. We have implemented a prototype tool for both T-OBDDs and T-SDDs on top of OBDD and SDD packages and the MathSAT SMT solver. Some preliminary empirical evaluation supports the effectiveness of the approach.

First-order probabilistic models combine the power of first-order logic, the de facto tool for handling relational structure, with probabilistic graphical models, the de facto tool for handling uncertainty. Lifted probabilistic inference algorithms for them have been the subject of much recent research. The main idea in these algorithms is to improve the accuracy and scalability of existing graphical models' inference algorithms by exploiting symmetry in the first-order representation. In this paper, we consider blocked Gibbs sampling, an advanced MCMC scheme, and lift it to the first-order level. We propose to achieve this by partitioning the first-order atoms in the model into a set of disjoint clusters such that exact lifted inference is polynomial in each cluster given an assignment to all other atoms not in the cluster. We propose an approach for constructing the clusters and show how it can be used to trade accuracy with computational complexity in a principled manner. Our experimental evaluation shows that lifted Gibbs sampling is superior to the propositional algorithm in terms of accuracy, scalability and convergence.

Propositional model counting (#SAT) can be solved efficiently when the input formula is in deterministic decomposable negation normal form (d-DNNF). Translating an arbitrary formula into a representation that allows inference tasks, such as counting, to be performed efficiently, is called knowledge compilation. Top-down knowledge compilation is a state-of-the-art technique for solving #SAT problems that leverages the traces of exhaustive DPLL search to obtain d-DNNF representations. While knowledge compilation is well studied for propositional approaches, knowledge compilation for the (quantifier free) counting modulo theory setting (#SMT) has been studied to a much lesser degree. In this paper, we discuss compilation strategies for #SMT. We specifically advocate for a top-down compiler based on the traces of exhaustive DPLL(T) search.

Deploying robots in real-world domains, such as households and flexible manufacturing lines, requires the robots to be taskable on demand. Linear temporal logic (LTL) is a widely-used specification language with a compositional grammar that naturally induces commonalities across tasks. However, the majority of prior research on reinforcement learning with LTL specifications treats every new formula independently. We propose LTL-Transfer, a novel algorithm that enables subpolicy reuse across tasks by segmenting policies for training tasks into portable transition-centric skills capable of satisfying a wide array of unseen LTL specifications while respecting safety-critical constraints. Experiments in a Minecraft-inspired domain show that LTL-Transfer can satisfy over 90% of 500 unseen tasks after training on only 50 task specifications and never violating a safety constraint. We also deployed LTL-Transfer on a quadruped mobile manipulator in an analog household environment to demonstrate its ability to transfer to many fetch and delivery tasks in a zero-shot fashion.

Multi-agent systems for resource allocation (MRAs) have been introduced as a concept for modelling competitive resource allocation problems in distributed computing. An MRA is composed of a set of agents and a set of resources. Each agent has goals in terms of allocating certain resources. For MRAs it is typically of importance that they are designed in a way such that there exists a strategy that guarantees that all agents will achieve their goals. The corresponding model checking problem is to determine whether such a winning strategy exists or not, and the synthesis problem is to actually build the strategy. While winning strategies ensure that all goals will be achieved, following such strategies does not necessarily involve an optimal use of resources. In this paper, we present a technique that allows to synthesise cost-optimal solutions to distributed resource allocation problems. We consider a scenario where system components such as agents and resources involve costs. A multi-agent system shall be designed that is cost-minimal but still capable of accomplishing a given set of goals. Our approach synthesises a winning strategy that minimises the cumulative costs of the components that are required for achieving the goals. The technique is based on a propositional logic encoding and a reduction of the synthesis problem to the maximum satisfiability problem (Max-SAT). Hence, a Max-SAT solver can be used to perform the synthesis. From a truth assignment that maximises the number of satisfied clauses of the encoding a cost-optimal winning strategy as well as a cost-optimal system can be immediately derived.

Motivating explanations in Bayesian networks using MAP-independence Johan Kwisthout We introduce MAP-independence as a novel concept in Bayesian networks, indicating potential impact of an intermediate (hidden) variable to the MAP explanation. We discuss how this concept may contribute to justifying MAP explanations, for example in the context of a decision support system. Abstract In decision support systems the motivation and justification of the system's diagnosis or classification is crucial for the acceptance of the system by the human user. In Bayesian networks a diagnosis or classification is typically formalized as the computation of the most probable joint value assignment to the hypothesis variables, given the observed values of the evidence variables (generally known as the MAP problem). While solving the MAP problem gives the most probable explanation of the evidence, the computation is a black box as far as the human user is concerned and it does not give additional insights that allow the user to appreciate and accept the decision. For example, a user might want to know to whether an unobserved variable could potentially (upon observation) impact the explanation, or whether it is irrelevant in this aspect.

Belief change studies how to update knowledge bases used for reasoning. Traditionally belief revision has been based on full propositional logic. However, reasoning with full propositional knowledge bases is computationally hard, whereas reasoning with Horn knowledge bases is fast. In the past several years, there has been considerable work in belief revision theory on developing a theory of belief contraction for knowledge represented in Horn form. Our main focus here is the computational complexity of belief contraction, and, in particular, of various methods and approaches suggested in the literature.