We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently, propositional, equalities on discrete sorts, and inequalities, more specifically difference arithmetic, on bounded integers). While many solutions to probabilistic inference over logic representations have been proposed, SGDPLL(T) is simultaneously (1) lifted, (2) exact and (3) modulo theories, that is, parameterized by a background logic theory. This offers a foundation for extending it to rich logic languages such as data structures and relational data. By lifted, we mean algorithms with constant complexity in the domain size (the number of values that variables can take). We also detail a solver for summations with difference arithmetic and show experimental results from a scenario in which SGDPLL(T) is much faster than a state-of-the-art probabilistic solver.
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic, called LTLf Modulo Theories (LTLfMT), is semi-decidable. Nevertheless, its high expressiveness comes useful in a number of use cases, such as model-checking of data-aware processes and data-aware planning. Despite the general undecidability of these problems, being able to solve satisfiable instances is a compromise worth studying. After motivating and descri…
Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this paper, we expand PIMT to a lifted version that also processes random functions and relations. This enhancement is achieved by adapting Inversion, a method from Lifted First-Order Probabilistic Inference literature, to also be modulo theories. This results in the first algorithm for exact probabilistic inference that efficiently and simultaneously exploits ran…
The design of embedded systems, that are ubiquitously used in mobile devices and cars, is becoming continuously more complex such that efficient system-level design methods are becoming crucial. My research aims at developing systems that help the designer express the complex design problem in a declarative way and explore the design space to obtain divers sets of solutions with desirable properties. To that end, we employ knowledge representation and reasoning capabilities of ASP in combination with background theories. As a result, for the first time, we proposed a sophisticated methodology …
Arizona State University（亚利桑那州立大学）；Houzz Inc.（Houzz 公司）
Both hybrid automata and action languages are formalisms for describing the evolution of dynamic systems. This paper establishes a formal relationship between them. We show how to succinctly represent hybrid automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories (ASPMT) --- an extension of answer set programs to the first-order level similar to the way satisfiability modulo theories (SMT) extends propositional satisfiability (SAT). We first show how to represent linear hybrid automata with convex invariants by an action langu…
University of Warsaw（华沙大学）；University of Bremen（不来梅大学）
The systematic modelling of \emph{dynamic spatial systems} [9] is a key requirement in a wide range of application areas such as comonsense cognitive robotics, computer-aided architecture design, dynamic geographic information systems. We present ASPMT(QS), a novel approach and fully-implemented prototype for non-monotonic spatial reasoning ---a crucial requirement within dynamic spatial systems-- based on Answer Set Programming Modulo Theories (ASPMT). ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Sat Modulo Theori…
Fondazione Bruno Kessler（布鲁诺·凯斯勒基金会）；Università degli Studi di Trento（特伦托大学）
Modelling problems containing a mixture of Boolean and numerical variables is a long-standing interest of Artificial Intelligence. However, performing inference and learning in hybrid domains is a particularly daunting task. The ability to model this kind of domains is crucial in "learning to design" tasks, that is, learning applications where the goal is to learn from examples how to perform automatic {\em de novo} design of novel objects. In this paper we present Structured Learning Modulo Theories, a max-margin approach for learning in hybrid domains based on Satisfiability Modulo Theories,…
RWTH Aachen University（亚琛工业大学）；University of Genoa（热那亚大学）
In manufacturing, the increasing involvement of autonomous robots in production processes poses new challenges on the production management. In this paper we report on the usage of Optimization Modulo Theories (OMT) to solve certain multi-robot scheduling problems in this area. Whereas currently existing methods are heuristic, our approach guarantees optimality for the computed solution. We do not only present our final method but also its chronological development, and draw some general observations for the development of OMT-based approaches.
The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Surprisingly, the problem of finding unsatisfiable cores in SMT has received very little attention in the literature. In this paper we present a novel approach to this problem, called the Lemma-Lifting approach. The main idea is …
The systematic modelling of dynamic spatial systems is a key requirement in a wide range of application areas such as commonsense cognitive robotics, computer-aided architecture design, and dynamic geographic information systems. We present ASPMT(QS), a novel approach and fully-implemented prototype for non-monotonic spatial reasoning -a crucial requirement within dynamic spatial systems- based on Answer Set Programming Modulo Theories (ASPMT). ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Satisfiability Modulo Theo…
IMDEA Software Institute（IMDEA软件研究所）；Cornell University（康奈尔大学）；University of California, Irvine（加州大学欧文分校）；The Hebrew University of Jerusalem（耶路撒冷希伯来大学）
This paper addresses a variant of multi-agent path finding (MAPF) in continuous space and time. We present a new solving approach based on satisfiability modulo theories (SMT) to obtain makespan optimal solutions. The standard MAPF is a task of navigating agents in an undirected graph from given starting vertices to given goal vertices so that agents do not collide with each other in vertices of the graph. In the continuous version (MAPF$^\mathcal{R}$) agents move in an $n$-dimensional Euclidean space along straight lines that interconnect predefined positions. For simplicity, we work with cir…
University of Calabria（卡拉布里亚大学）；Free University of Bozen-Bolzano（博岑-博尔扎诺自由大学）
Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the \Godel and \Luka fuzzy connectives are usually considered, due to their properties. Although the \Godel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. %, even if bodies are restricted to \Luka or \Godel conjunct…
Recent work on weighted model counting has been very successfully applied to the problem of probabilistic inference in Bayesian networks. The probability distribution is encoded into a Boolean normal form and compiled to a target language, in order to represent local structure expressed among conditional probabilities more efficiently. We show that further improvements are possible, by exploiting the knowledge that is lost during the encoding phase and incorporating it into a compiler inspired by Satisfiability Modulo Theories. Constraints among variables are used as a background theory, which…
Hashing-based model counting has emerged as a promising approach for large-scale probabilistic inference on graphical models. A key component of these techniques is the use of xor-based 2-universal hash functions that operate over Boolean domains. Many counting problems arising in probabilistic inference are, however, naturally encoded over finite discrete domains. Techniques based on bit-level (or Boolean) hash functions require these problems to be propositionalized, making it impossible to leverage the remarkable progress made in SMT (Satisfiability Modulo Theory) solvers that can reason di…
Continuous Optimization for Satisfiability Modulo Theories on Linear Real Arithmetic
Department of Electrical and Computer Engineering, National University of Singapore, Singapore（电子与计算机工程系，新加坡国立大学）；School of Computing and Data Science, The University of Hong Kong, Hong Kong, China（计算与数据科学学院，香港大学）
We address item relocation problems in graphs in this paper. We assume items placed in vertices of an undirected graph with at most one item per vertex. Items can be moved across edges while various constraints depending on the type of relocation problem must be satisfied. We introduce a general problem formulation that encompasses known types of item relocation problems such as multi-agent path finding (MAPF) and token swapping (TSWAP). In this formulation we express two new types of relocation problems derived from token swapping that we call token rotation (TROT) and token permutation (TPER…
We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.
PAGODA (Probabilistic Autonomous Goal-Directed Agent) is a model for autonomous learning in probabilistic domains [desJardins, 1992] that incorporates innovative techniques for using the agent's existing knowledge to guide and constrain the learning process and for representing, reasoning with, and learning probabilistic knowledge. This paper describes the probabilistic representation and inference mechanism used in PAGODA. PAGODA forms theories about the effects of its actions and the world state on the environment over time. These theories are represented as conditional probability distribut…
Technische Universität Dortmund（多特蒙德工业大学）；Università degli Studi di Trento（特伦托大学）
This paper introduces CLEO, a novel preference elicitation algorithm capable of recommending complex objects in hybrid domains, characterized by both discrete and continuous attributes and constraints defined over them. The algorithm assumes minimal initial information, i.e., a set of catalog attributes, and defines decisional features as logic formulae combining Boolean and algebraic constraints over the attributes. The (unknown) utility of the decision maker (DM) is modelled as a weighted combination of features. CLEO iteratively alternates a preference elicitation step, where pairs of candi…
In this paper, we take a fresh look at three Popperian concepts: riskiness, falsifiability, and truthlikeness (or verisimilitude) of scientific hypotheses or theories. First, we make explicit the dimensions that underlie the notion of riskiness. Secondly, we examine if and how degrees of falsifiability can be defined, and how they are related to various dimensions of the concept of riskiness as well as the experimental context. Thirdly, we consider the relation of riskiness to (expected degrees of) truthlikeness. Throughout, we pay special attention to probabilistic theories and we offer a ten…
University of Melbourne（墨尔本大学）；KTH Royal Institute of Technology（KTH皇家理工学院）
This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum cost paths over the geometric graphs selected by PRM. Cuts eliminate paths that cannot be mapped into smooth plans that satisfy suitably defined kinematic constraints. We generate candidate smooth plans by fitting splines to vertices in minimum-cost path. Plans are validated with a recently proposed algorithm that maps them into finite traces, without need …
