High-Fidelity Vector Space Models of Structured Data

Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued vector of a fixed, pre-specified size. In this work, we introduce a novel approach that compiles structured data into a satisfiability problem which has in its set of solutions at least (and often only) the input data. The satisfiability problem is constructed from constraints which are generated automatically a priori from a given signature, thus trivially allowing for a bag-of-words-esque vector representation of the input to be constructed. The method is demonstrated in two areas, automated reasoning and natural language processing, where it is shown to produce vector representations of natural-language sentences and first-order logic clauses that can be precisely translated back to their original, structured input forms.Comment: updated to reflect conference submission, new experiment adde

Relational Characterisations of Paths

Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in many areas of mathematics and computing, researchers usually fall back to point-wise reasoning when it comes to arguments about paths in a graph. We present a purely algebraic way to specify different kinds of paths in relation algebras. We study the relationship between paths with a designated root vertex and paths without such a vertex. Since we stay in first-order logic this development helps with mechanising proofs.To demonstrate the applicability of the algebraic framework we verify the correctness of three basic graph algorithms. All results of this paper are formally verified using the interactive proof assistant Isabelle/HOL

Algebraic Net Class Rewriting Systems, Syntax and Semantics for Knowledge Representation and Automated Problem Solving

The intention of the present study is to establish general framework for automated problem solving by approaching the task universal algebraically introducing knowledge as realizations of generalized free algebra based nets, graphs with gluing forms connecting in- and out-edges to nodes. Nets are caused to undergo transformations in conceptual level by type wise differentiated intervening net rewriting systems dispersing problems to abstract parts, matching being determined by substitution relations. Achieved sets of conceptual nets constitute congruent classes. New results are obtained within construction of problem solving systems where solution algorithms are derived parallel with other candidates applied to the same net classes. By applying parallel transducer paths consisting of net rewriting systems to net classes congruent quotient algebras are established and the manifested class rewriting comprises all solution candidates whenever produced nets are in anticipated languages liable to acceptance of net automata

Handling Nominals and Inverse Roles using Algebraic Reasoning

This paper presents a novel SHOI tableau calculus which incorporates algebraic reasoning for deciding ontology consistency. Numerical restrictions imposed by nominals, existential and universal restrictions are encoded into a set of linear inequalities. Column generation and branch-and-price algorithms are used to solve these inequalities. Our preliminary experiments indicate that this calculus performs better on SHOI ontologies than standard tableau methods.Comment: 23 page

Interpretable Feature Recommendation for Signal Analytics

This paper presents an automated approach for interpretable feature recommendation for solving signal data analytics problems. The method has been tested by performing experiments on datasets in the domain of prognostics where interpretation of features is considered very important. The proposed approach is based on Wide Learning architecture and provides means for interpretation of the recommended features. It is to be noted that such an interpretation is not available with feature learning approaches like Deep Learning (such as Convolutional Neural Network) or feature transformation approaches like Principal Component Analysis. Results show that the feature recommendation and interpretation techniques are quite effective for the problems at hand in terms of performance and drastic reduction in time to develop a solution. It is further shown by an example, how this human-in-loop interpretation system can be used as a prescriptive system.Comment: 4 pages, Interpretable Data Mining Workshop, CIKM 201

KBLRN : End-to-End Learning of Knowledge Base Representations with Latent, Relational, and Numerical Features

We present KBLRN, a framework for end-to-end learning of knowledge base representations from latent, relational, and numerical features. KBLRN integrates feature types with a novel combination of neural representation learning and probabilistic product of experts models. To the best of our knowledge, KBLRN is the first approach that learns representations of knowledge bases by integrating latent, relational, and numerical features. We show that instances of KBLRN outperform existing methods on a range of knowledge base completion tasks. We contribute a novel data sets enriching commonly used knowledge base completion benchmarks with numerical features. The data sets are available under a permissive BSD-3 license. We also investigate the impact numerical features have on the KB completion performance of KBLRN.Comment: UAI 201

Logic for approximate entailment in ordered universes of discourse

The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an order structure. The chosen framework is designed in view of possible applications

Fail better: What formalized math can teach us about learning

Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in as much detail as our need for eliminating risk might require. For those who do not happen to have direct access to the realm of mathematical truths, the modern field of formalized mathematics has quite a few lessons to contribute, and one might pay heed to what it has to say, for instance, about: the importance of employing proof strategies; the fine control of automation in unraveling the structure of a certain proof object; reasoning forward from the givens and backward from the goals, in developing proof scripts; knowing when and how definitions and identities apply in a helpful way, and when they do not apply; seeing proofs [and refutations] as dynamical objects, not reflected by the static derivation trees that Proof Theory wants them to be. I believe that the great challenge for teachers and learners resides currently less on the availability of suitable generic tools than in combining them wisely in view of their preferred education paradigms and introducing them in a way that best fits their specific aims, possibly with the help of intelligent online interactive tutoring systems. As a proof of concept, a computerized proof assistant that makes use of several successful tools already freely available on the market and that takes into account some of the above findings about teaching and learning Logic is hereby introduced. To fully account for our informed intuitions on the subject it would seem that a little bit extra technology would still be inviting, but no major breakthrough is really needed: We are talking about tools that are already within our reach to develop, as the fruits of collaborative effort.Comment: Proceedings of the Fourth International Conference on Tools for Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M. Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat, Fran\c{c}ois Schwarzentrube

Multi-Object Reasoning with Constrained Goal Models

Goal models have been widely used in Computer Science to represent software requirements, business objectives, and design qualities. Existing goal modelling techniques, however, have shown limitations of expressiveness and/or tractability in coping with complex real-world problems. In this work, we exploit advances in automated reasoning technologies, notably Satisfiability and Optimization Modulo Theories (SMT/OMT), and we propose and formalize: (i) an extended modelling language for goals, namely the Constrained Goal Model (CGM), which makes explicit the notion of goal refinement and of domain assumption, allows for expressing preferences between goals and refinements, and allows for associating numerical attributes to goals and refinements for defining constraints and optimization goals over multiple objective functions, refinements and their numerical attributes; (ii) a novel set of automated reasoning functionalities over CGMs, allowing for automatically generating suitable refinements of input CGMs, under user-specified assumptions and constraints, that also maximize preferences and optimize given objective functions. We have implemented these modelling and reasoning functionalities in a tool, named CGM-Tool, using the OMT solver OptiMathSAT as automated reasoning backend. Moreover, we have conducted an experimental evaluation on large CGMs to support the claim that our proposal scales well for goal models with thousands of elements.Comment: 52 pages (with appendices). Under journal submissio

Towards Bit-Width-Independent Proofs in SMT Solvers

Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we propose a translation from bit-vector formulas of non-fixed bit-width to formulas in a logic supported by SMT solvers that includes non-linear integer arithmetic, uninterpreted functions, and universal quantification. While this logic is undecidable, this approach can still solve many formulas by capitalizing on advancements in SMT solving for non-linear arithmetic and universally quantified formulas. We provide several case studies in which we have applied this approach with promising results, including the bit-width independent verification of invertibility conditions, compiler optimizations, and bit-vector rewrites