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  • On the Weisfeiler-Leman Dimension of Finite Groups
    arXiv.cs.LO Pub Date : 2020-03-30
    Jendrik Brachter; Pascal Schweitzer

    In comparison to graphs, combinatorial methods for the isomorphism problem of finite groups are less developed than algebraic ones. To be able to investigate the descriptive complexity of finite groups and the group isomorphism problem, we define the Weisfeiler-Leman algorithm for groups. In fact we define three versions of the algorithm. In contrast to graphs, where the three analogous versions readily

    更新日期:2020-04-01
  • VC density of set systems defnable in tree-like graphs
    arXiv.cs.LO Pub Date : 2020-03-31
    Adam Paszke; Michał Pilipczuk

    We study set systems definable in graphs using variants of logic with different expressive power. Our focus is on the notion of Vapnik-Chervonenkis density: the smallest possible degree of a polynomial bounding the cardinalities of restrictions of such set systems. On one hand, we prove that if $\varphi(\bar x,\bar y)$ is a fixed CMSO$_1$ formula and $\cal C$ is a class of graphs with uniformly bounded

    更新日期:2020-04-01
  • Verification of Nonblockingness in Bounded Petri Nets: A Novel Semi-Structural Approach
    arXiv.cs.LO Pub Date : 2020-03-31
    Chao Gu; Ziyue Ma; Zhiwu Li; Alessandro Giua

    This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We provide an algorithm to construct a novel structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking

    更新日期:2020-04-01
  • UTxO- vs account-based smart contract blockchain programming paradigms
    arXiv.cs.LO Pub Date : 2020-03-31
    Lars Brunjes; Murdoch J. Gabbay

    We implement two versions of a simple but paradigmatic smart contract: one in Solidity on the Ethereum blockchain platform, and one in Plutus on the Cardano platform, giving annotated code excerpts, with full source code also attached. We get a clearer view of the Cardano programming model in particular by introducing a simple but novel mathematical abstraction which we call idealised Cardano. For

    更新日期:2020-04-01
  • Fusible numbers and Peano Arithmetic
    arXiv.cs.LO Pub Date : 2020-03-31
    Jeff Erickson; Gabriel Nivasch; Junyan Xu

    Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: $0$ is fusible, and whenever $x,y$ are fusible with $|y-x|<1$, the number $(x+y+1)/2$ is also fusible. We prove that the set of fusible numbers, ordered by the usual order on $\mathbb R$, is well-ordered, with order type $\varepsilon_0$. Furthermore, we prove that the density of the fusible numbers along

    更新日期:2020-04-01
  • An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)
    arXiv.cs.LO Pub Date : 2018-09-12
    Willem Conradie; Salih Durhan; Guido Sciavicco

    There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent result by Balbiani, Goranko, and Sciavicco presented an explicit two-sorted point-interval temporal framework in which time instants (points) and time periods (intervals)

    更新日期:2020-04-01
  • Combined Covers and Beth Definability (Extended Version)
    arXiv.cs.LO Pub Date : 2019-11-18
    Diego Calvanese; Silvio Ghilardi; Alessandro Gianola; Marco Montali; Andrey Rivkin

    In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we proved in a previous paper that covers are strictly related to model completions, a well-known topic in model theory. In this paper we investigate cover transfer to theory combinations in the disjoint

    更新日期:2020-04-01
  • How to reason with inconsistent probabilistic information?
    arXiv.cs.LO Pub Date : 2020-03-28
    Marta Bílková; Sabine Frittella; Ondrej Majer; Sajad Nazari

    A recent line of research has developed around logics of belief based on information confirmed by a reliable source. In this paper, we provide a finer analysis and extension of this framework, where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature. We combine Belnap-Dunn logic and non-standard probabilities to account for potentially contradictory information

    更新日期:2020-03-31
  • On amenability of constraint satisfaction problems
    arXiv.cs.LO Pub Date : 2020-03-29
    Michał R. Przybyłek

    Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern model theory. The aim of this paper is threefold. (1) We give a simple purely-logical proof of the claim and show that the advanced results from topology and model

    更新日期:2020-03-31
  • Bisimulation as a Logical Relation
    arXiv.cs.LO Pub Date : 2020-03-30
    Claudio Hermida; Uday Reddy; Edmund Robinson; Alessio Santamaria

    We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system, and the general result is that a relation $R$ between two transition systems on state spaces $S$ and $T$ is a bisimulation if and only if the derived algebraic structures

    更新日期:2020-03-31
  • Dual-Context Calculi for Modal Logic
    arXiv.cs.LO Pub Date : 2016-02-15
    G. A. Kavvos

    We present and discuss natural deduction systems and associated modal lambda calculi for constructive variants of the necessity fragments of the modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of assumptions, one of which can be thought as modal, and the other as intuitionistic. We show that these calculi have their roots in patterns found

    更新日期:2020-03-31
  • Complete algorithms for algebraic strongest postconditions and weakest preconditions in polynomial ODEs
    arXiv.cs.LO Pub Date : 2017-08-17
    Michele Boreale

    A system of polynomial ordinary differential equations (ODEs) is specified via a vector of multivariate polynomials, or vector field, $F$. A safety assertion $\psi\rightarrow[F]\phi$ means that the trajectory of the system will lie in a subset $\phi$ (the postcondition) of the state-space, whenever the initial state belongs to a subset $\psi$ (the precondition). We consider the case when $\phi$ and

    更新日期:2020-03-31
  • Tight Polynomial Worst-Case Bounds for Loop Programs
    arXiv.cs.LO Pub Date : 2019-06-24
    Amir M. Ben-Amram; Geoff Hamilton

    In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth

    更新日期:2020-03-31
  • Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
    arXiv.cs.LO Pub Date : 2019-02-08
    Ross Duncan; Aleks Kissinger; Simon Perdrix; John van de Wetering

    We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using the rules of the ZX-calculus, we give a simplification strategy for ZX-diagrams based on the two graph transformations of local complementation and

    更新日期:2020-03-31
  • Towards Logical Specification of Statistical Machine Learning
    arXiv.cs.LO Pub Date : 2019-07-24
    Yusuke Kawamoto

    We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, robustness, and fairness of classifiers by using epistemic logic. Then we show some relationships among properties of classifiers and those between classification

    更新日期:2020-03-31
  • Metamath Zero: The Cartesian Theorem Prover
    arXiv.cs.LO Pub Date : 2019-10-22
    Mario Carneiro

    As the usage of theorem prover technology expands, so too does the reliance on correctness of the tools. Metamath Zero is a verification system that aims for simplicity of logic and implementation, without compromising on efficiency of verification. It is formally specified in its own language, and supports a number of translations to and from other proof languages. This paper describes the abstract

    更新日期:2020-03-31
  • No-Go Theorems for Distributive Laws
    arXiv.cs.LO Pub Date : 2020-03-27
    Maaike Zwart; Dan Marsden

    Monads are commonplace in computer science, and can be composed using Beck's distributive laws. Unfortunately, finding distributive laws can be extremely difficult and error-prone. The literature contains some general principles for constructing distributive laws. However, until now there have been no such techniques for establishing when no distributive law exists. We present three families of theorems

    更新日期:2020-03-30
  • Splitting Epistemic Logic Programs
    arXiv.cs.LO Pub Date : 2018-12-20
    Pedro Cabalar; Jorge Fandinno; Luis Fariñas del Cerro

    Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all stable models or in some stable model. As it can be imagined, the associated semantics has proved to be non-trivial, as the truth of the subjective literal may interfere

    更新日期:2020-03-30
  • Choice functions based on sets of strict partial orders: an axiomatic characterisation
    arXiv.cs.LO Pub Date : 2020-03-25
    Jasper De Bock

    Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of this form. It includes as special cases an axiomatic characterisation for choice functions based on (sets of) total orders, (sets of) weak orders, (sets of) coherent lower previsions

    更新日期:2020-03-28
  • Benchmarking Software Model Checkers on Automotive Code
    arXiv.cs.LO Pub Date : 2020-03-26
    Lukas Westhofen; Philipp Berger; Joost-Pieter Katoen

    This paper reports on our experiences with verifying automotive C code by state-of-the-art open source software model checkers. The embedded C code is automatically generated from Simulink open-loop controller models. Its diverse features (decision logic, floating-point and pointer arithmetic, rate limiters and state-flow systems) and the extensive use of floating-point variables make verifying the

    更新日期:2020-03-28
  • Regular partitions of gentle graphs
    arXiv.cs.LO Pub Date : 2020-03-26
    Yiting Jiang; Jaroslav Nesetril; Patrice Ossona de Mendez; Sebastian Siebertz

    Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems

    更新日期:2020-03-28
  • No-Rainbow Problem is NP-Hard
    arXiv.cs.LO Pub Date : 2020-03-26
    Dmitriy Zhuk

    Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints. In this paper we show that one of the most popular variants of the SCSP, called No-Rainbow Problem, is NP-Hard.

    更新日期:2020-03-28
  • Applying the Isabelle Insider Framework to Airplane Security
    arXiv.cs.LO Pub Date : 2020-03-26
    Florian Kammüller; Manfred Kerber

    Avionics is one of the fields in which verification methods have been pioneered and brought a new level of reliability to systems used in safety critical environments. Tragedies, like the 2015 insider attack on a German airplane, in which all 150 people on board died, show that safety and security crucially depend not only on the well functioning of systems but also on the way how humans interact with

    更新日期:2020-03-28
  • Founded Semantics and Constraint Semantics of Logic Rules
    arXiv.cs.LO Pub Date : 2016-06-20
    Yanhong A. Liu; Scott D. Stoller

    Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs, including in attempting to solve the well-known Russell's paradox. These semantics are often non-intuitive and hard-to-understand when unrestricted negation is used in recursion

    更新日期:2020-03-28
  • Polyteam Semantics
    arXiv.cs.LO Pub Date : 2017-04-07
    Miika Hannula; Juha Kontinen; Jonni Virtema

    Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define "Polyteam Semantics" in which formulae are evaluated over a family of teams. We begin

    更新日期:2020-03-28
  • High-level signatures and initial semantics
    arXiv.cs.LO Pub Date : 2018-05-09
    Benedikt Ahrens; André Hirschowitz; Ambroise Lafont; Marco Maggesi

    We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of signature for specifying syntactic constructions. In the spirit of Initial Semantics, we define the syntax generated by a signature to be the initial object---if it exists---in a suitable category of models. In our framework, the existence of an

    更新日期:2020-03-28
  • A Nonexistence Certificate for Projective Planes of Order Ten with Weight 15 Codewords
    arXiv.cs.LO Pub Date : 2019-11-11
    Curtis Bright; Kevin Cheung; Brett Stevens; Dominique Roy; Ilias Kotsireas; Vijay Ganesh

    Using techniques from the fields of symbolic computation and satisfiability checking we verify one of the cases used in the landmark result that projective planes of order ten do not exist. In particular, we show that there exist no projective planes of order ten that generate codewords of weight fifteen, a result first shown in 1973 via an exhaustive computer search. We provide a simple satisfiability

    更新日期:2020-03-28
  • Modal Logics for Nominal Transition Systems
    arXiv.cs.LO Pub Date : 2019-04-04
    Joachim Parrow; Johannes Borgström; Lars-Henrik Eriksson; Ramūnas Forsberg Gutkovas; Tjark Weber

    We define a general notion of transition system where states and action labels can be from arbitrary nominal sets, actions may bind names, and state predicates from an arbitrary logic define properties of states. A Hennessy-Milner logic for these systems is introduced, and proved adequate and expressively complete for bisimulation equivalence. A main technical novelty is the use of finitely supported

    更新日期:2020-03-28
  • A Journey into Ontology Approximation: From Non-Horn to Horn
    arXiv.cs.LO Pub Date : 2020-01-21
    Anneke Haga; Carsten Lutz; Johannes Marti; Frank Wolter

    We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe that in the $\mathcal{ELU}$-to-$\mathcal{EL}$ case finite approximations tend to exist in practice and are guaranteed to exist when the original ontology is acyclic

    更新日期:2020-03-28
  • A Formalization of SQL with Nulls
    arXiv.cs.LO Pub Date : 2020-03-25
    Wilmer Ricciotti; James Cheney

    SQL is the world's most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal specification. Commercial SQL implementations interpret the standard in different ways, so that, given the same input data, the same query can yield different results depending

    更新日期:2020-03-26
  • Topology and adjunction in promise constraint satisfaction
    arXiv.cs.LO Pub Date : 2020-03-25
    Andrei Krokhin; Jakub Opršal; Marcin Wrochna; Stanislav Živný

    The approximate graph colouring problem concerns colouring a $k$-colourable graph with $c$ colours, where $c\geq k$. This problem naturally generalises to promise graph homomorphism and further to promise constraint satisfaction problems. Complexity analysis of all these problems is notoriously difficult. In this paper, we introduce two new techniques to analyse the complexity of promise CSPs: one

    更新日期:2020-03-26
  • Vector logic and counterfactuals
    arXiv.cs.LO Pub Date : 2020-03-09
    Eduardo Mizraji

    In this work we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vectors formalism for logical functions and truth values. With this formalism, we can describe the counterfactuals as complex matrix operators that appear preprocessing the implication matrix with one of the square roots of the negation, a complex matrix. This mathematical approach puts in

    更新日期:2020-03-26
  • Two Formal Systems of the $λδ$ Family Revised
    arXiv.cs.LO Pub Date : 2019-11-28
    Ferruccio Guidi

    We present the framework $\lambda\delta$-2B that significantly improves and generalizes two previous formal systems of the $\lambda\delta$ family, i.e., $\lambda\delta$-1A and $\lambda\delta$-2A. Our main contributions are, on the one hand, a short definition for the framework and, on the other hand, some important results that we are presenting here for the first time. The definition stands just on

    更新日期:2020-03-26
  • Cartesian bicategories with choice
    arXiv.cs.LO Pub Date : 2020-03-20
    Filippo Bonchi; Jens Seeber; Pawel Sobocinski

    Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent applications. The passage between a category and its bicategory of relations is an important question that has been widely studied for decades. We study an alternative

    更新日期:2020-03-24
  • Temporal Conjunctive Query Answering in the Extended DL-Lite Family
    arXiv.cs.LO Pub Date : 2020-03-20
    Stefan Borgwardt; Veronika Thost

    Ontology-based query answering (OBQA) augments classical query answering in databases by domain knowledge encoded in an ontology. Systems for OBQA use the ontological knowledge to infer new information that is not explicitly given in the data. Moreover, they usually employ the open-world assumption, which means that knowledge that is not stated explicitly in the data and that is not inferred is not

    更新日期:2020-03-24
  • Partial Quantifier Elimination By Certificate Clauses
    arXiv.cs.LO Pub Date : 2020-03-21
    Eugene Goldberg

    We study a modification of the Quantifier Elimination (QE) problem called Partial QE (PQE) for propositional CNF formulas. In PQE, only a small subset of target clauses is taken out of the scope of quantifiers. The appeal of PQE is that many verification problems, e.g. equivalence checking and model checking, reduce to PQE and, intuitively, the latter should be much easier than QE. One can perform

    更新日期:2020-03-24
  • Kontrol Edilebilir ptSTL Formulu Sentezi -- Synthesis of Controllable ptSTL Formulas
    arXiv.cs.LO Pub Date : 2020-03-22
    Irmak Saglam; Ebru Aydin Gol

    In this work, we develop an approach to anomaly detection and prevention problem using Signal Temporal Logic (STL). This approach consists of two steps: detection of the causes of the anomalities as STL formulas and prevention of the satisfaction of the formula via controller synthesis. This work focuses on the first step and proposes a formula template such that any controllable cause can be represented

    更新日期:2020-03-24
  • A Trustful Monad for Axiomatic Reasoning with Probability and Nondeterminism
    arXiv.cs.LO Pub Date : 2020-03-22
    Reynald Affeldt; Jacques Garrigue; David Nowak; Takafumi Saikawa

    The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization (the first one to the best of our knowledge) in the Coq proof assistant of a monad equipped with both choices: the geometrically convex monad. This formalization has an immediate application: it provides a model for

    更新日期:2020-03-24
  • A CSP implementation of the directed bigraph embedding problem
    arXiv.cs.LO Pub Date : 2020-03-19
    Alessio Chiapperini; Marino Miculan; Marco Peressotti

    Directed bigraphs are a meta-model which generalises Milner's bigraphs by taking into account the request flow between controls and names. A key problem about these bigraphs is that of bigraph embedding, i.e., finding the embeddings of a bigraph inside a larger one.We present an algorithm for computing embeddings of directed bigraphs, via a reduction to a constraint satisfaction problem. We prove soundness

    更新日期:2020-03-24
  • Dichotomy between deterministic and probabilistic models in countably additive effectus theory
    arXiv.cs.LO Pub Date : 2020-03-23
    Kenta Cho; Bas Westerbaan; John van de Wetering

    Effectus theory is a relatively new approach to categorical logic that can be seen as an abstract form of generalized probabilistic theories (GPTs). While the scalars of a GPT are always the real unit interval $[0,1]$, in an effectus they can form any effect monoid. Hence, there are quite exotic effectuses resulting from more pathological effect monoids. In this paper we introduce $\sigma$-effectuses

    更新日期:2020-03-24
  • Beyond sets with atoms: definability in first order logic
    arXiv.cs.LO Pub Date : 2020-03-10
    Michał R. Przybyłek

    Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite structures to some infinite structures. Recent results show that this is indeed possible and leads to many practical applications. In this paper we shall take another

    更新日期:2020-03-24
  • The Strahler number of a parity game
    arXiv.cs.LO Pub Date : 2020-03-19
    Laure Daviaud; Marcin Jurdziński; K. S. Thejaswini

    The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices~$n$ and linear in $({d}/{2k})^k$

    更新日期:2020-03-20
  • Abstraction, Up-to Techniques and Games for Systems of Fixpoint Equations
    arXiv.cs.LO Pub Date : 2020-03-19
    Paolo Baldan; Barbara König; Tommaso Padoan

    Systems of fixpoint equations over complete lattices, consisting of (mixed) least and greatest fixpoint equations, allow one to express a number of verification tasks such as model-checking of various kinds of specification logics or the check of coinductive behavioural equivalences. In this paper we develop a theory of approximation for systems of fixpoint equations in the style of abstract interpretation:

    更新日期:2020-03-20
  • Automated Formal Synthesis of Lyapunov Neural Networks
    arXiv.cs.LO Pub Date : 2020-03-19
    Alessandro Abate; Daniele Ahmed; Mirco Giacobbe; Andrea Peruffo

    We propose an automated and sound technique to synthesize provably correct Lyapunov functions. We exploit a counterexample-guided approach composed of two parts: a learner provides candidate Lyapunov functions, and a verifier either guarantees the correctness of the candidate or offers counterexamples, which are used incrementally to further guide the synthesis of Lyapunov functions. Whilst the verifier

    更新日期:2020-03-20
  • Counting Bounded Tree Depth Homomorphisms
    arXiv.cs.LO Pub Date : 2020-03-18
    Martin Grohe

    We prove that graphs G, G' satisfy the same sentences of first-order logic with counting of quantifier rank at most k if and only if they are homomorphism-indistinguishable over the class of all graphs of tree depth at most k. Here G, G' are homomorphism-indistinguishable over a class C of graphs if for each graph F in C, the number of homomorphisms from F to G equals the number of homomorphisms from

    更新日期:2020-03-19
  • Axiom Pinpointing
    arXiv.cs.LO Pub Date : 2020-03-18
    Rafael Peñaloza

    Axiom pinpointing refers to the task of finding the specific axioms in an ontology which are responsible for a consequence to follow. This task has been studied, under different names, in many research areas, leading to a reformulation and reinvention of techniques. In this work, we present a general overview to axiom pinpointing, providing the basic notions, different approaches for solving it, and

    更新日期:2020-03-19
  • Foundations of Explainable Knowledge-Enabled Systems
    arXiv.cs.LO Pub Date : 2020-03-17
    Shruthi Chari; Daniel M. Gruen; Oshani Seneviratne; Deborah L. McGuinness

    Explainability has been an important goal since the early days of Artificial Intelligence. Several approaches for producing explanations have been developed. However, many of these approaches were tightly coupled with the capabilities of the artificial intelligence systems at the time. With the proliferation of AI-enabled systems in sometimes critical settings, there is a need for them to be explainable

    更新日期:2020-03-18
  • Directions for Explainable Knowledge-Enabled Systems
    arXiv.cs.LO Pub Date : 2020-03-17
    Shruthi Chari; Daniel M. Gruen; Oshani Seneviratne; Deborah L. McGuinness

    Interest in the field of Explainable Artificial Intelligence has been growing for decades and has accelerated recently. As Artificial Intelligence models have become more complex, and often more opaque, with the incorporation of complex machine learning techniques, explainability has become more critical. Recently, researchers have been investigating and tackling explainability with a user-centric

    更新日期:2020-03-18
  • Construe: a software solution for the explanation-based interpretation of time series
    arXiv.cs.LO Pub Date : 2020-03-17
    Tomas Teijeiro; Paulo Felix

    This paper presents a software implementation of a general framework for time series interpretation based on abductive reasoning. The software provides a data model and a set of algorithms to make inference to the best explanation of a time series, resulting in a description in multiple abstraction levels of the processes underlying the time series. As a proof of concept, a comprehensive knowledge

    更新日期:2020-03-18
  • Formal Scenario-Based Testing of Autonomous Vehicles: From Simulation to the Real World
    arXiv.cs.LO Pub Date : 2020-03-17
    Daniel J. Fremont; Edward Kim; Yash Vardhan Pant; Sanjit A. Seshia; Atul Acharya; Xantha Bruso; Paul Wells; Steve Lemke; Qiang Yu; Shalin Mehta

    We present a new approach to automated scenario-based testing of the safety of autonomous vehicles, especially those using advanced artificial intelligence-based components, spanning both simulation-based evaluation as well as testing in the real world. Our approach is based on formal methods, combining formal specification of scenarios and safety properties, algorithmic test case generation using

    更新日期:2020-03-18
  • Towards a Uniform Theory of Effectful State Machines
    arXiv.cs.LO Pub Date : 2014-01-21
    Sergey Goncharov; Stefan Milius; Alexandra Silva

    Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs' notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual

    更新日期:2020-03-18
  • On the Strong Equivalences for LPMLN Programs
    arXiv.cs.LO Pub Date : 2019-09-09
    Bin Wang; Jun Shen; Shutao Zhang; Zhizheng Zhang

    LPMLN is a powerful knowledge representation and reasoning tool that combines the non-monotonic reasoning ability of Answer Set Programming (ASP) and the probabilistic reasoning ability of Markov Logic Networks (MLN). In this paper, we study the strong equivalence for LPMLN programs, which is an important tool for program rewriting and theoretical investigations in the field of logic programming.First

    更新日期:2020-03-18
  • Abstract Argumentation and the Rational Man
    arXiv.cs.LO Pub Date : 2019-11-29
    Timotheus Kampik; Juan Carlos Nieves

    Abstract argumentation has emerged as a method for non-monotonic reasoning that has gained tremendous traction in the symbolic artificial intelligence community. In the literature, the different approaches to abstract argumentation that were refined over the years are typically evaluated from a logics perspective; an analysis that is based on models of ideal, rational decision-making does not exist

    更新日期:2020-03-18
  • Reachability is Tower Complete
    arXiv.cs.LO Pub Date : 2020-03-13
    Yuxi Fu; Qizhe Yang

    A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete.

    更新日期:2020-03-16
  • Experimental Evaluation of a Method to Simplify Expressions
    arXiv.cs.LO Pub Date : 2020-03-13
    Baudouin Le Charlier

    We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in practice, in spite of its great generality. We first recall the notion of a collection of structures, which allows us to manipulate very large (possibly infinite) sets of

    更新日期:2020-03-16
  • Comb Diagrams for Discrete-Time Feedback
    arXiv.cs.LO Pub Date : 2020-03-13
    Mario Román

    The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing "holes" or "incomplete parts", sometimes known as comb diagrams. We give a possible formalization of what these circuits with incomplete parts represent in terms of symmetric monoidal categories, using the dinaturality equivalence

    更新日期:2020-03-16
  • Causal Unfoldings and Disjunctive Causes
    arXiv.cs.LO Pub Date : 2020-03-12
    Marc de Visme; Glynn Winskel

    In the simplest form of event structure, a prime event structure, an event is associated with a unique causal history, its prime cause. However, it is quite common for an event to have disjunctive causes in that it can be enabled by any one of multiple sets of causes. Sometimes the sets of causes may be mutually exclusive, inconsistent one with another, and sometimes not, in which case they coexist

    更新日期:2020-03-16
  • Animated Logic: Correct Functional Conversion to Conjunctive Normal Form
    arXiv.cs.LO Pub Date : 2020-03-11
    Pedro Barroso; Mário Pereira; António Ravara

    We present an approach to obtain formally verified implementations of classical Computational Logic algorithms. We choose the Why3 platform because it allows to implement functions in a style very close to the mathematical definitions, as well as it allows a high degree of automation in the verification process. As proof of concept, we present a mathematical definition of the algorithm to convert propositional

    更新日期:2020-03-12
  • Interval Temporal Logic Decision Tree Learning
    arXiv.cs.LO Pub Date : 2020-03-10
    Andrea Brunello; Guido Sciavicco; Ionel Eduard Stan

    Decision trees are simple, yet powerful, classification models used to classify categorical and numerical data, and, despite their simplicity, they are commonly used in operations research and management, as well as in knowledge mining. From a logical point of view, a decision tree can be seen as a structured set of logical rules written in propositional logic. Since knowledge mining is rapidly evolving

    更新日期:2020-03-12
  • Magic: the Gathering is as Hard as Arithmetic
    arXiv.cs.LO Pub Date : 2020-03-11
    Stella Biderman

    Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the computational complexity of playing Magic optimally. In this paper we show that the ``mate-in-$n$'' problem for Magic is $\Delta^0_n$-hard and that optimal play in two-player

    更新日期:2020-03-12
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