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 Logic & Formal Reasoning


Can Machines Design? An Artificial General Intelligence Approach

arXiv.org Artificial Intelligence

Can machines design? Can they come up with creative solutions to problems and build tools and artifacts across a wide range of domains? Recent advances in the field of computational creativity and formal Artificial General Intelligence (AGI) provide frameworks for machines with the general ability to design. In this paper we propose to integrate a formal computational creativity framework into the G\"odel machine framework. We call the resulting framework design G\"odel machine. Such a machine could solve a variety of design problems by generating novel concepts. In addition, it could change the way these concepts are generated by modifying itself. The design G\"odel machine is able to improve its initial design program, once it has proven that a modification would increase its return on the utility function. Finally, we sketch out a specific version of the design G\"odel machine which specifically addresses the design of complex software and hardware systems. Future work aims at the development of a more formal version of the design G\"odel machine and a proof of concept implementation.


Compiling Probabilistic Model Checking into Probabilistic Planning

AAAI Conferences

It has previously been observed that the verification of safety properties in deterministic model-checking frameworks can be compiled into classical planning. A similar connection exists between goal probability analysis on either side, yet that connection has not been explored. We fill that gap with a translation from Jani, an input language for quantitative model checkers including the Modest toolset and PRISM, into PPDDL. Our experiments motivate further cross-fertilization between both research areas, specifically the exchange of algorithms. Our study also initiates the creation of new benchmarks for goal probability analysis.


Weighted Abstract Dialectical Frameworks: Extended and Revised Report

arXiv.org Artificial Intelligence

Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.


SMarTplan: a Task Planner for Smart Factories

arXiv.org Artificial Intelligence

Smart factories are on the verge of becoming the new industrial paradigm, wherein optimization permeates all aspects of production, from concept generation to sales. To fully pursue this paradigm, flexibility in the production means as well as in their timely organization is of paramount importance. AI is planning a major role in this transition, but the scenarios encountered in practice might be challenging for current tools. Task planning is one example where AI enables more efficient and flexible operation through an online automated adaptation and rescheduling of the activities to cope with new operational constraints and demands. In this paper we present SMarTplan, a task planner specifically conceived to deal with real-world scenarios in the emerging smart factory paradigm. Including both special-purpose and general-purpose algorithms, SMarTplan is based on current automated reasoning technology and it is designed to tackle complex application domains. In particular, we show its effectiveness on a logistic scenario, by comparing its specialized version with the general purpose one, and extending the comparison to other state-of-the-art task planners.


ML + FV = $\heartsuit$? A Survey on the Application of Machine Learning to Formal Verification

arXiv.org Artificial Intelligence

Formal Verification (Fv) and Machine Learning (Ml) can seem incompatible due to their opposite mathematical foundations and their use in real-life problems: Fv mostly relies on discrete mathematics and aims at ensuring correctness; Ml often relies on probabilistic models and consists of learning patterns from training data. In this paper, we postulate that they are complementary in practice, and explore how Ml helps Fv in its classical approaches: static analysis, model-checking, theorem-proving, and Sat solving. We draw a landscape of the current practice and catalog some of the most prominent uses of Ml inside Fv tools, thus offering a new perspective on Fv techniques that can help researchers and practitioners to better locate the possible synergies. We discuss lessons learned from our work, point to possible improvements and offer visions for the future of the domain in the light of the science of software and systems modeling.


Constructing Datasets for Multi-hop Reading Comprehension Across Documents

arXiv.org Artificial Intelligence

Most Reading Comprehension methods limit themselves to queries which can be answered using a single sentence, paragraph, or document. Enabling models to combine disjoint pieces of textual evidence would extend the scope of machine comprehension methods, but currently there exist no resources to train and test this capability. We propose a novel task to encourage the development of models for text understanding across multiple documents and to investigate the limits of existing methods. In our task, a model learns to seek and combine evidence - effectively performing multi-hop (alias multi-step) inference. We devise a methodology to produce datasets for this task, given a collection of query-answer pairs and thematically linked documents. Two datasets from different domains are induced, and we identify potential pitfalls and devise circumvention strategies. We evaluate two previously proposed competitive models and find that one can integrate information across documents. However, both models struggle to select relevant information, as providing documents guaranteed to be relevant greatly improves their performance. While the models outperform several strong baselines, their best accuracy reaches 42.9% compared to human performance at 74.0% - leaving ample room for improvement.


MEBN-RM: A Mapping between Multi-Entity Bayesian Network and Relational Model

arXiv.org Machine Learning

Multi-Entity Bayesian Network (MEBN) is a knowledge representation formalism combining Bayesian Networks (BN) with First-Order Logic (FOL). MEBN has sufficient expressive power for general-purpose knowledge representation and reasoning. Developing a MEBN model to support a given application is a challenge, requiring definition of entities, relationships, random variables, conditional dependence relationships, and probability distributions. When available, data can be invaluable both to improve performance and to streamline development. By far the most common format for available data is the relational database (RDB). Relational databases describe and organize data according to the Relational Model (RM). Developing a MEBN model from data stored in an RDB therefore requires mapping between the two formalisms. This paper presents MEBN-RM, a set of mapping rules between key elements of MEBN and RM. We identify links between the two languages (RM and MEBN) and define four levels of mapping from elements of RM to elements of MEBN. These definitions are implemented in the MEBN-RM algorithm, which converts a relational schema in RM to a partial MEBN model. Through this research, the software has been released as a MEBN-RM open-source software tool. The method is illustrated through two example use cases using MEBN-RM to develop MEBN models: a Critical Infrastructure Defense System and a Smart Manufacturing System.


Model-free, Model-based, and General Intelligence

arXiv.org Artificial Intelligence

During the 60s and 70s, AI researchers explored intuitions about intelligence by writing programs that displayed intelligent behavior. Many good ideas came out from this work but programs written by hand were not robust or general. After the 80s, research increasingly shifted to the development of learners capable of inferring behavior and functions from experience and data, and solvers capable of tackling well-defined but intractable models like SAT, classical planning, Bayesian networks, and POMDPs. The learning approach has achieved considerable success but results in black boxes that do not have the flexibility, transparency, and generality of their model-based counterparts. Model-based approaches, on the other hand, require models and scalable algorithms. Model-free learners and model-based solvers have close parallels with Systems 1 and 2 in current theories of the human mind: the first, a fast, opaque, and inflexible intuitive mind; the second, a slow, transparent, and flexible analytical mind. In this paper, I review developments in AI and draw on these theories to discuss the gap between model-free learners and model-based solvers, a gap that needs to be bridged in order to have intelligent systems that are robust and general.


Constrained Counting and Sampling: Bridging the Gap between Theory and Practice

arXiv.org Artificial Intelligence

Constrained counting and sampling are two fundamental problems in Computer Science with numerous applications, including network reliability, privacy, probabilistic reasoning, and constrained-random verification. In constrained counting, the task is to compute the total weight, subject to a given weighting function, of the set of solutions of the given constraints. In constrained sampling, the task is to sample randomly, subject to a given weighting function, from the set of solutions to a set of given constraints. Consequently, constrained counting and sampling have been subject to intense theoretical and empirical investigations over the years. Prior work, however, offered either heuristic techniques with poor guarantees of accuracy or approaches with proven guarantees but poor performance in practice. In this thesis, we introduce a novel hashing-based algorithmic framework for constrained sampling and counting that combines the classical algorithmic technique of universal hashing with the dramatic progress made in combinatorial reasoning tools, in particular, SAT and SMT, over the past two decades. The resulting frameworks for counting (ApproxMC2) and sampling (UniGen) can handle formulas with up to million variables representing a significant boost up from the prior state of the art tools' capability to handle few hundreds of variables. If the initial set of constraints is expressed as Disjunctive Normal Form (DNF), ApproxMC is the only known Fully Polynomial Randomized Approximation Scheme (FPRAS) that does not involve Monte Carlo steps. By exploiting the connection between definability of formulas and variance of the distribution of solutions in a cell defined by 3-universal hash functions, we introduced an algorithmic technique, MIS, that reduced the size of XOR constraints employed in the underlying universal hash functions by as much as two orders of magnitude.


Program Synthesis from Visual Specification

arXiv.org Artificial Intelligence

Program synthesis is the process of automatically translating a specification into computer code. Traditional synthesis settings require a formal, precise specification. Motivated by computer education applications where a student learns to code simple turtle-style drawing programs, we study a novel synthesis setting where only a noisy user-intention drawing is specified. This allows students to sketch their intended output, optionally together with their own incomplete program, to automatically produce a completed program. We formulate this synthesis problem as search in the space of programs, with the score of a state being the Hausdorff distance between the program output and the user drawing. We compare several search algorithms on a corpus consisting of real user drawings and the corresponding programs, and demonstrate that our algorithms can synthesize programs optimally satisfying the specification.