Logic & Formal Reasoning



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This is one of only a handful couple of writings that consolidates three fundamental postulations in the investigation of rationale programming: the logic that gives logic programs their extraordinary character: the act of programming viably utilizing the logic; and the productive usage of logic software on PCs.


Polynomial-time probabilistic reasoning with partial observations via implicit learning in probability logics

arXiv.org Artificial Intelligence

Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which efficient algorithms are generally not known. In this work we consider the use of bounded-degree fragments of the "sum-of-squares" logic as a probability logic. Prior work has shown that we can decide refutability for such fragments in polynomial-time. We propose to use such fragments to answer queries about whether a given probability distribution satisfies a given system of constraints and bounds on expected values. We show that in answering such queries, such constraints and bounds can be implicitly learned from partial observations in polynomial-time as well. It is known that this logic is capable of deriving many bounds that are useful in probabilistic analysis. We show here that it furthermore captures useful polynomial-time fragments of resolution. Thus, these fragments are also quite expressive.


Automatic White-Box Testing of First-Order Logic Ontologies

arXiv.org Artificial Intelligence

Formal ontologies are axiomatizations in a logic-based formalism. The development of formal ontologies, and their important role in the Semantic Web area, is generating considerable research on the use of automated reasoning techniques and tools that help in ontology engineering. One of the main aims is to refine and to improve axiomatizations for enabling automated reasoning tools to efficiently infer reliable information. Defects in the axiomatization can not only cause wrong inferences, but can also hinder the inference of expected information, either by increasing the computational cost of, or even preventing, the inference. In this paper, we introduce a novel, fully automatic white-box testing framework for first-order logic ontologies. Our methodology is based on the detection of inference-based redundancies in the given axiomatization. The application of the proposed testing method is fully automatic since a) the automated generation of tests is guided only by the syntax of axioms and b) the evaluation of tests is performed by automated theorem provers. Our proposal enables the detection of defects and serves to certify the grade of suitability --for reasoning purposes-- of every axiom. We formally define the set of tests that are generated from any axiom and prove that every test is logically related to redundancies in the axiom from which the test has been generated. We have implemented our method and used this implementation to automatically detect several non-trivial defects that were hidden in various first-order logic ontologies. Throughout the paper we provide illustrative examples of these defects, explain how they were found, and how each proof --given by an automated theorem-prover-- provides useful hints on the nature of each defect. Additionally, by correcting all the detected defects, we have obtained an improved version of one of the tested ontologies: Adimen-SUMO.


CASP Solutions for Planning in Hybrid Domains

arXiv.org Artificial Intelligence

CASP is an extension of ASP that allows for numerical constraints to be added in the rules. PDDL+ is an extension of the PDDL standard language of automated planning for modeling mixed discrete-continuous dynamics. In this paper, we present CASP solutions for dealing with PDDL+ problems, i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP CASP solver in order to solve CASP programs arising from PDDL+ domains. An experimental analysis, performed on well-known linear and non-linear variants of PDDL+ domains, involving various configurations of the EZCSP solver, other CASP solvers, and PDDL+ planners, shows the viability of our solution.


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.


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.


Technical Report: Inconsistency in Answer Set Programs and Extensions

arXiv.org Artificial Intelligence

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. HEX-programs extend ASP with external atoms for accessing arbitrary external information, which can introduce values that do not appear in the input program. In this work we consider inconsistent ASP- and HEX-programs, i.e., programs without answer sets. We study characterizations of inconsistency, introduce a novel notion for explaining inconsistencies in terms of input facts, analyze the complexity of reasoning tasks in context of inconsistency analysis, and present techniques for computing inconsistency reasons. This theoretical work is motivated by two concrete applications, which we also present. The first one is the new modeling technique of query answering over subprograms as a convenient alternative to the well-known saturation technique. The second application is a new evaluation algorithm for HEX-programs based on conflict-driven learning for programs with multiple components: while for certain program classes previous techniques suffer an evaluation bottleneck, the new approach shows significant, potentially exponential speedup in our experiments. Since well-known ASP extensions such as constraint ASP and DL-programs correspond to special cases of HEX, all presented results are interesting beyond the specific formalism.


DeepLogic: End-to-End Logical Reasoning

arXiv.org Artificial Intelligence

Neural networks have been learning complex multi-hop reasoning in various domains. One such formal setting for reasoning, logic, provides a challenging case for neural networks. In this article, we propose a Neural Inference Network (NIN) for learning logical inference over classes of logic programs. Trained in an end-to-end fashion NIN learns representations of normal logic programs, by processing them at a character level, and the reasoning algorithm for checking whether a logic program entails a given query. We define 12 classes of logic programs that exemplify increased level of complexity of the inference process (multi-hop and default reasoning) and show that our NIN passes 10 out of the 12 tasks. We also analyse the learnt representations of logic programs that NIN uses to perform the logical inference.