A decidable weakening of Compass Logic based on cone-shaped cardinal directions

We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening of Venema's Compass Logic. We prove that, unlike Compass Logic and other projection-based spatial logics, its satisfiability problem is decidable (precisely, PSPACE-complete). We also show that it is expressive enough to capture meaningful interval temporal logics - in particular, the interval temporal logic of Allen's relations "Begins", "During", and "Later", and their transposes

Automatic inference of specifications using matching logic

Formal specifications can be used for various software engineering activities ranging from finding errors to documenting software and automatic test-case generation. Automatically discovering specifications for heap-manipulating programs is a challenging task. In this paper, we propose a technique for automatically inferring formal specifications from C code which is based on the symbolic execution and automated reasoning tandem "MATCHING LOGIC /K framework". We implemented our technique for a fragment of C, called KERNELC, in the automated tool KINDSPEC, which generates axioms that describe the precise input/output behavior of C routines that handle pointer-based structures, i.e., result values and state change. These specifications can be written either in MATCHING LOGIC itself, which is useful for further automated analysis within the K formal environment, or in sugared axiomatic form, which favors better human inspection. Since we rely on rewriting logic K semantics specification of programming languages, our approach can be easily extended to any language for which a formal semantics in K is given.This work has been partially supported by the EU (FEDER) and the Spanish MEC/MICINN, ref. TIN 2010-21062-C02-0, and by Generalitat Valenciana, ref. PROMETEO 2011/052.Alpuente Frasnedo, M.; Feliú Gabaldón, MA.; Villanueva García, A. (2013). Automatic inference of specifications using matching logic. En Proceeding PEPM '13 Proceedings of the ACM SIGPLAN 2013 workshop on Partial evaluation and program manipulation. Association for Computing Machinery (ACM). 127-136. https://doi.org/10.1145/2426890.2426914S12713

Graph Neural Networks as the Copula Mundi between Logic and Machine Learning: A Roadmap

Combining machine learning (ML) and computational logic (CL) is hard, mostly because of the inherently- different ways they use to represent knowledge. In fact, while ML relies on fixed-size numeric repre- sentations leveraging on vectors, matrices, or tensors of real numbers, CL relies on logic terms and clauses—which are unlimited in size and structure. Graph neural networks (GNN) are a novelty in the ML world introduced for dealing with graph- structured data in a sub-symbolic way. In other words, GNN pave the way towards the application of ML to logic clauses and knowledge bases. However, there are several ways to encode logic knowledge into graphs: which is the best one heavily depends on the specific task at hand. Accordingly, in this paper, we (i) elicit a number of problems from the field of CL that may benefit from many graph-related problems where GNN has been proved effective; (ii) exemplify the application of GNN to logic theories via an end-to-end toy example, to demonstrate the many intricacies hidden behind the technique; (iii) discuss the possible future directions of the application of GNN to CL in general, pointing out opportunities and open issues

Introduction to the Neoclassical Interpretation: Quantum Steampunk

In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based “Hydrodynamic” treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for free space and these physics are interchangeable with modern methods for treating superfluid-like continuums. Thus the mathematical equivalence of the methods do not comprise alternative physics but an alternative interpretation of the same physics. Though many individual components describing a “neo-aether” or “quintessence” are available, an overarching structural outline of how these tools can work together to provide an alternative working overview of modern physics has remained undefined. This paper will propose a set of introductory concepts in the first outline of a toy model which will later connect the alternative tools and conceptualizations with their modern counterparts. This introductory paper provides the simpler “100-miles out” overview of the whole of physics from this perspective, in an easily comprehensible, familiar and intuitive, informal dialog fashion. While this paper grants the largest and loosest introductory overview, subsequent papers in this series will address the finite connections between modern physics and this hydrodynamic view

Spectral and polarization effects in deterministically nonperiodic multilayers containing optically anisotropic and gyrotropic materials

Influence of material anisotropy and gyrotropy on optical properties of fractal multilayer nanostructures is theoretically investigated. Gyrotropy is found to uniformly rotate the output polarization for bi-isotropic multilayers of arbitrary geometrical structure without any changes in transmission spectra. When introduced in a polarization splitter based on a birefringent fractal multilayer, isotropic gyrotropy is found to resonantly alter output polarizations without shifting of transmission peak frequencies. The design of frequency-selective absorptionless polarizers for polarization-sensitive integrated optics is outlined

Full contract verification for ATL using symbolic execution

The Atlas Transformation Language (ATL) is currently one of the most used model transformation languages and has become a de facto standard in model-driven engineering for implementing model transformations. At the same time, it is understood by the community that enhancing methods for exhaustively verifying such transformations allows for a more widespread adoption of model-driven engineering in industry. A variety of proposals for the verification of ATL transformations have arisen in the past few years. However, the majority of these techniques are either based on non-exhaustive testing or on proof methods that require human assistance and/or are not complete. In this paper, we describe our method for statically verifying the declarative subset of ATL model transformations. This verification is performed by translating the transformation (including features like filters, OCL expressions, and lazy rules) into our model transformation language DSLTrans. As we handle only the declarative portion of ATL, and DSLTrans is Turing-incomplete, this reduction in expressivity allows us to use a symbolic-execution approach to generate representations of all possible input models to the transformation. We then verify pre-/post-condition contracts on these representations, which in turn verifies the transformation itself. The technique we present in this paper is exhaustive for the subset of declarative ATL model transformations. This means that if the prover indicates a contract holds on a transformation, then the contract’s pre-/post-condition pair will be true for any input model for that transformation. We demonstrate and explore the applicability of our technique by studying several relatively large and complex ATL model transformations, including a model transformation developed in collaboration with our industrial partner. As well, we present our ‘slicing’ technique. This technique selects only those rules in the DSLTrans transformation needed for contract proof, thereby reducing proving timeComisión Interministerial de Ciencia y Tecnología TIN2015-70560-RJunta de Andalucía P10-TIC-5906Junta de Andalucía P12-TIC-186