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  • Universal Algebra in UniMath
    arXiv.cs.LO Pub Date : 2020-07-09
    Gianluca Amato; Marco Maggesi; Maurizio Parton; Cosimo Perini Brogi

    We present an ongoing effort to implement Universal Algebra in the UniMath system. Our aim is to develop a general framework for formalizing and studying Universal Algebra in a proof assistant. By constituting a formal system for isolating the invariants of the theory we are interested in -- that is, general algebraic structures modulo isomorphism -- Univalent Mathematics seems to provide a suitable

    更新日期:2020-07-10
  • Logic of computational semi-effects and categorical gluing for equivariant functors
    arXiv.cs.LO Pub Date : 2020-07-09
    Yuichi Nishiwaki; Toshiya Asai

    In this paper, we revisit Moggi's celebrated calculus of computational effects from the perspective of logic of monoidal action (actegory). Our development takes the following steps. Firstly, we perform proof-theoretic reconstruction of Moggi's computational metalanguage and obtain a type theory with a modal type $\rhd$ as a refinement. Through the proposition-as-type paradigm, its logic can be seen

    更新日期:2020-07-10
  • Treewidth-Aware Complexity in ASP: Not all Positive Cycles are Equally Hard
    arXiv.cs.LO Pub Date : 2020-07-09
    Markus Hecher; Jorge Fandinno

    It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential time in the worst case. The exponential time hypothesis (ETH) implies that this result is tight for SAT, that is, SAT cannot be solved in subexponential time. This

    更新日期:2020-07-10
  • Symbolic Reachability Analysis of High Dimensional Max-Plus Linear Systems
    arXiv.cs.LO Pub Date : 2020-07-09
    Muhammad Syifa'ul Mufid; Dieky Adzkiya; Alessandro Abate

    This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify whether there exist trajectories of the MPL system that, starting from the initial set, eventually reach the target set. We show that RA can be solved symbolically

    更新日期:2020-07-10
  • Recursion and evolution: Part II
    arXiv.cs.LO Pub Date : 2020-06-12
    Alexandros Arvanitakis

    We examine the question of whether it is possible for a diagonalizing system, to learn to use environmental reward and punishment as an information, in order to appropriately adapt. More specifically, we study the possiblity of such a system, to learn to use diagonalization on the basis of a rewarding function. Relevant phenomena regarding memory are also investigated.

    更新日期:2020-07-10
  • Explainability of Intelligent Transportation Systems using Knowledge Compilation: a Traffic Light Controller Case
    arXiv.cs.LO Pub Date : 2020-07-09
    Salomón Wollenstein-Betech; Christian Muise; Christos G. Cassandras; Ioannis Ch. Paschalidis; Yasaman Khazaeni

    Usage of automated controllers which make decisions on an environment are widespread and are often based on black-box models. We use Knowledge Compilation theory to bring explainability to the controller's decision given the state of the system. For this, we use simulated historical state-action data as input and build a compact and structured representation which relates states with actions. We implement

    更新日期:2020-07-10
  • Closure hyperdoctrines, with paths
    arXiv.cs.LO Pub Date : 2020-07-08
    Davide Castelnovo; Marino Miculan

    Spatial logics are modal logics whose modalities are interpreted using topological concepts of neighbourhood and connectivity. Recently, these logics have been extended to (pre)closure spaces, a generalization of topological spaces covering also the notion of neighbourhood in discrete structures. In this paper we introduce an abstract theoretical framework for the systematic investigation of the logical

    更新日期:2020-07-09
  • Certifying Emptiness of Timed Büchi Automata
    arXiv.cs.LO Pub Date : 2020-07-08
    Simon Wimmer; Frédéric Herbreteau; Jaco van de Pol

    Model checkers for timed automata are widely used to verify safety-critical, real-time systems. State-of-the-art tools achieve scalability by intricate abstractions. We aim at further increasing the trust in their verification results, in particular for checking liveness properties. To this end, we develop an approach for extracting certificates for the emptiness of timed B\"uchi automata from model

    更新日期:2020-07-09
  • On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic
    arXiv.cs.LO Pub Date : 2020-07-08
    Miika Hannula; Juha Kontinen; Martin Lück; Jonni Virtema

    Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to term constructions, 2) restrictions to the form of the Boolean matrix. Of the first sort, we consider two kinds of restrictions: firstly, disallowing nested use of

    更新日期:2020-07-09
  • The Scattering Compositional Learner: Discovering Objects, Attributes, Relationships in Analogical Reasoning
    arXiv.cs.LO Pub Date : 2020-07-08
    Yuhuai Wu; Honghua Dong; Roger Grosse; Jimmy Ba

    In this work, we focus on an analogical reasoning task that contains rich compositional structures, Raven's Progressive Matrices (RPM). To discover compositional structures of the data, we propose the Scattering Compositional Learner (SCL), an architecture that composes neural networks in a sequence. Our SCL achieves state-of-the-art performance on two RPM datasets, with a 48.7% relative improvement

    更新日期:2020-07-09
  • Study on Computational Thinking as Problem-solving Skill: Comparison Based on Students Mindset in Engineering and Social Science
    arXiv.cs.LO Pub Date : 2020-07-08
    Andik Asmara

    One of the capabilities which 21st-century skill compulsory a person is critical thinking and problem-solving skill that becomes top positions rank. Focus on problem-solving skills can be taught to a child, especially begun in elementary school refer to prior research focus on K-12. Computational thinking was one problem-solving skill that popular to implemented and studied in the current decade. This

    更新日期:2020-07-09
  • The Vectorial Lambda Calculus Revisited
    arXiv.cs.LO Pub Date : 2020-07-07
    Alejandro Díaz-Caro; Francisco Noriega

    We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vectorial (as well as Lineal) was originally meant for quantum computing, as an extension to System F where linear combinations of lambda terms are also terms and linear combinations of types are also types. In its first presentation, Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised

    更新日期:2020-07-08
  • Colored props for large scale graphical reasoning
    arXiv.cs.LO Pub Date : 2020-07-07
    Titouan Carette; Simon Perdrix

    The prop formalism allows representation of processes withstring diagrams and has been successfully applied in various areas such as quantum computing, electric circuits and control flow graphs. However, these graphical approaches suffer from scalability problems when it comes to writing large diagrams. A proposal to tackle this issue has been investigated for ZX-calculus using colored props. This

    更新日期:2020-07-08
  • Multi-player Equilibria Verification for Concurrent Stochastic Games
    arXiv.cs.LO Pub Date : 2020-07-07
    Marta Kwiatkowska; Gethin Norman; David Parker; Gabriel Santos

    Concurrent stochastic games (CSGs) are an ideal formalism for modelling probabilistic systems that feature multiple players or components with distinct objectives making concurrent, rational decisions. Examples include communication or security protocols and multi-robot navigation. Verification methods for CSGs exist but are limited to scenarios where agents or players are grouped into two coalitions

    更新日期:2020-07-08
  • A Myhill-Nerode Theorem for Register Automata and Symbolic Trace Languages
    arXiv.cs.LO Pub Date : 2020-07-07
    Frits Vaandrager; Abhisek Midya

    We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by this run. Our main result is a generalization of the classical Myhill-Nerode theorem to this symbolic setting. Our generalization requires the use of three relations

    更新日期:2020-07-08
  • Automated Formal Synthesis of Neural Barrier Certificates for Dynamical Models
    arXiv.cs.LO Pub Date : 2020-07-07
    Andrea Peruffo; Daniele Ahmed; Alessandro Abate

    We introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. The approach is underpinned by an inductive framework: this is structured as a sequential loop between a learner, which manipulates a candidate BC as a neural network, and a sound verifier, which either certifies through algorithmic

    更新日期:2020-07-08
  • On LTL Model Checking for Low-Dimensional Discrete Linear Dynamical Systems
    arXiv.cs.LO Pub Date : 2020-07-06
    Toghrul Karimov; Joël Ouaknine; James Worrell

    Consider a discrete dynamical system given by a square matrix $M \in \mathbb{Q}^{d \times d}$ and a starting point $s \in \mathbb{Q}^d$. The orbit of such a system is the infinite trajectory $\langle s, Ms, M^2s, \ldots\rangle$. Given a collection $T_1, T_2, \ldots, T_m \subseteq \mathbb{R}^d$ of semialgebraic sets, we can associate with each $T_i$ an atomic proposition $P_i$ which evaluates to true

    更新日期:2020-07-07
  • Living Without Beth and Craig: Explicit Definitions and Interpolants in Description Logics with Nominals
    arXiv.cs.LO Pub Date : 2020-07-06
    Alessandro Artale; Jean Christoph Jung; Andrea Mazzullo; Ana Ozaki; Frank Wolter

    The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The Beth definability property (BDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, they transform potentially hard existence problems into deduction problems in the underlying logic. Description Logics with nominals do not have the CIP

    更新日期:2020-07-07
  • Simulation-Guided Boolean Resubstitution
    arXiv.cs.LO Pub Date : 2020-07-06
    Siang-Yun Lee; Heinz Riener; Alan Mishchenko; Robert K. Brayton; Giovanni De Micheli

    This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to demonstrate the effectiveness of the proposed approach. Methods to generate highly expressive simulation patterns are developed, and the generated patterns are used in resubstitution

    更新日期:2020-07-07
  • Enhancing SAT solvers with glue variable predictions
    arXiv.cs.LO Pub Date : 2020-07-06
    Jesse Michael Han

    Modern SAT solvers routinely operate at scales that make it impractical to query a neural network for every branching decision. NeuroCore, proposed by Selsam and Bjorner, offered a proof-of-concept that neural networks can still accelerate SAT solvers by only periodically refocusing a score-based branching heuristic. However, that work suffered from several limitations: their modified solvers require

    更新日期:2020-07-07
  • Inferences and Modal Vocabulary
    arXiv.cs.LO Pub Date : 2020-07-06
    Florian Richter

    Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g. abductive inferences. The debate between advocates and critics of abduction as a useful instrument can be reconstructed along the issue, how an abductive inference

    更新日期:2020-07-07
  • Logic, Language, and Calculus
    arXiv.cs.LO Pub Date : 2020-07-06
    Florian Richter

    The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is argued that inferential relations in a metalanguage (like a calculus for propositional logic) cannot represent conceptual relations of natural language. Inferential

    更新日期:2020-07-07
  • INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving
    arXiv.cs.LO Pub Date : 2020-07-06
    Yuhuai Wu; Albert Jiang; Jimmy Ba; Roger Grosse

    In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to test agents' generalization ability. INT is based on a procedure for generating theorems and proofs; this procedure's knobs allow us to measure 6 different types of

    更新日期:2020-07-07
  • A Framework for Modelling, Verification and Transformation of Concurrent Imperative Programs
    arXiv.cs.LO Pub Date : 2020-07-05
    Maksym Bortin

    The paper gives a comprehensive presentation of a framework, embedded into the simply typed higher-order logic, and aimed at providing a sound assistance in formal reasoning about models of imperative programs with interleaved computations. As a case study, a model of the Peterson's mutual exclusion algorithm will be scrutinised in the course of the paper illustrating applicability of the framework

    更新日期:2020-07-07
  • An interpretation of dependent type theory in a model category of locally cartesian closed categories
    arXiv.cs.LO Pub Date : 2020-07-06
    Martin E. Bidlingmaier

    Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the "gros" semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with the structure of a model of dependent type theory. The original

    更新日期:2020-07-07
  • Dynamic Awareness
    arXiv.cs.LO Pub Date : 2020-07-06
    Joseph Y. Halpern; Evan Piermont

    We investigate how to model the beliefs of an agent who becomes more aware. We use the framework of Halpern and Rego (2013) by adding probability, and define a notion of a model transition that describes constraints on how, if an agent becomes aware of a new formula $\phi$ in state $s$ of a model $M$, she transitions to state $s^*$ in a model $M^*$. We then discuss how such a model can be applied to

    更新日期:2020-07-07
  • Separating Positive and Negative Data Examples by Concepts and Formulas: The Case of Restricted Signatures
    arXiv.cs.LO Pub Date : 2020-07-06
    Jean Christoph Jung; Carsten Lutz; Hadrien Pulcini; Frank Wolter

    We study the separation of positive and negative data examples in terms of description logic (DL) concepts and formulas of decidable FO fragments, in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols from the data and ontology that can be used for separation. We consider weak and strong versions of the resulting problem that differ

    更新日期:2020-07-07
  • Supervisory Controller Synthesis for Non-terminating Processes is an Obliging Game
    arXiv.cs.LO Pub Date : 2020-07-03
    Rupak Majumdar; Anne-Kathrin Schmuck

    We present a new algorithm to solve the supervisory control problem over non-terminating processes modeled as $\omega$-regular automata. A solution to the problem was obtained by Thistle in 1995 which uses complex manipulations of automata. This algorithm is notoriously hard to understand and, to the best of our knowledge, has never been implemented. We show a new solution to the problem through a

    更新日期:2020-07-06
  • Probabilistic Soft Type Assignment
    arXiv.cs.LO Pub Date : 2020-07-03
    Gianluca Curzi; Luca Roversi

    We model randomized complexity classes in the style of Implicit Computational Complexity. We introduce PSTA, a probabilistic version of STA, the type-theoretical counterpart of Soft Linear Logic. PSTA is a type assignment for an extension of Simpson's Linear Lambda Calculus and its surface reduction, where Linear additives express random choice. Linear additives are weaker than the usual ones; they

    更新日期:2020-07-06
  • Many-Sorted Hybrid Modal Languages
    arXiv.cs.LO Pub Date : 2020-07-02
    Ioana Leuştean; Natalia Moangă; Traian Florin Şerbănuţă

    We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of the full logic, for which we prove sound and complete deduction and we show that it is powerful enough to represent both the programs and their semantics in an uniform

    更新日期:2020-07-06
  • Active learning of timed automata with unobservable resets
    arXiv.cs.LO Pub Date : 2020-07-03
    Léo Henry; Nicolas Markey; Thierry Jéron

    Active learning of timed languages is concerned with the inference of timed automata from observed timed words. The agent can query for the membership of words in the target language, or propose a candidate model and verify its equivalence to the target. The major difficulty of this framework is the inference of clock resets, central to the dynamics of timed automata, but not directly observable. Interesting

    更新日期:2020-07-06
  • Logical Separability of Incomplete Data under Ontologies
    arXiv.cs.LO Pub Date : 2020-07-03
    Jean Christoph Jung; Carsten Lutz; Hadrien Pulcini; Frank Wolter

    Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, and generating referring expressions. In this paper, we investigate the existence of a separating formula for incomplete data in the presence of an ontology. Both for the ontology language and

    更新日期:2020-07-06
  • Living without Beth and Craig: Explicit Definitions and Interpolants in the Guarded Fragment
    arXiv.cs.LO Pub Date : 2020-07-03
    Jean Christoph Jung; Frank Wolter

    The guarded fragment of FO fails to have the Craig Interpolation Property (CIP) and the Projective Beth Definability Property (PBDP). Thus, not every valid implication between guarded formulas has a guarded interpolant, and not every implicitly definable relation has an explicit guarded definition. In this article, we show that nevertheless the existence of guarded interpolants and explicit definitions

    更新日期:2020-07-06
  • Smt-Switch: a solver-agnostic C++ API for SMT Solving
    arXiv.cs.LO Pub Date : 2020-07-02
    Makai Mann; Amalee Wilson; Cesare Tinelli; Clark Barrett

    This extended abstract describes work in progress on Smt-Switch, an open-source, solver-agnostic API for SMT solving. Smt-Switch provides an abstract interface, which can be implemented by different SMT solvers. Smt-Switch provides simple, uniform, and high-performance access to SMT solving for applications in areas such as automated reasoning, planning, and formal verification. The interface allows

    更新日期:2020-07-06
  • The combined basic LP and affine IP relaxation for promise VCSPs on infinite domains
    arXiv.cs.LO Pub Date : 2020-07-03
    Caterina Viola; Stanislav Zivny

    Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming

    更新日期:2020-07-06
  • Analysing Spatial Properties on Neighbourhood Spaces
    arXiv.cs.LO Pub Date : 2020-07-02
    Sven Linker; Fabio Papacchini; Michele Sevegnani

    We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces. We show that this notion, path preserving bisimulation, preserves formulas of the spatial logic SLCS. We then use this preservation result to show that SLCS cannot express standard topological properties such as separation and connectedness. Furthermore, we compare the bisimulation relation with standard

    更新日期:2020-07-03
  • "Most of" leads to undecidability: Failure of adding frequencies to LTL
    arXiv.cs.LO Pub Date : 2020-07-02
    Bartosz Bednarczyk; Jakub Michaliszyn

    Linear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not yet fully explored. The main goal of this work is to study the effect of adding weak forms of percentage constraints (e.g. that most of the positions in the past

    更新日期:2020-07-03
  • Characteristic Logics for Behavioural Metrics via Fuzzy Lax Extensions
    arXiv.cs.LO Pub Date : 2020-07-02
    Paul Wild; Lutz Schröder

    Behavioural distances provide a fine-grained measure of equivalence in systems involving quantitative data, such as probabilistic, fuzzy, or metric systems. Like in the classical setting of crisp bisimulation-type equivalences, the wide variation found in system types creates a need for generic methods that apply to many system types at once. Approaches of this kind are emerging within the paradigm

    更新日期:2020-07-03
  • Context Graphs for Legal Reasoning and Argumentation
    arXiv.cs.LO Pub Date : 2020-07-01
    Max Rapp; Axel Adrian; Michael Kohlhase

    We propose a new, structured, logic-based framework for legal reasoning and argumentation: Instead of using a single, unstructured meaning space, theory graphs organize knowledge and inference into collections of modular meaning spaces organized by inheritance and interpretation. Context graphs extend theory graphs by attack relations and interpret theories as knowledge contexts of agents in argumentation

    更新日期:2020-07-03
  • Verifiably Safe Exploration for End-to-End Reinforcement Learning
    arXiv.cs.LO Pub Date : 2020-07-02
    Nathan Hunt; Nathan Fulton; Sara Magliacane; Nghia Hoang; Subhro Das; Armando Solar-Lezama

    Deploying deep reinforcement learning in safety-critical settings requires developing algorithms that obey hard constraints during exploration. This paper contributes a first approach toward enforcing formal safety constraints on end-to-end policies with visual inputs. Our approach draws on recent advances in object detection and automated reasoning for hybrid dynamical systems. The approach is evaluated

    更新日期:2020-07-03
  • Higher-order Logic as Lingua Franca -- Integrating Argumentative Discourse and Deep Logical Analysis
    arXiv.cs.LO Pub Date : 2020-07-02
    David Fuenmayor; Christoph Benzmüller

    We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its expressivity this logic can adopt the status of a uniform \textit{lingua franca} allowing the encoding of both formalized arguments (their deep logical structure) and dialectical

    更新日期:2020-07-03
  • Signature-Based Abduction for Expressive Description Logics -- Technical Report
    arXiv.cs.LO Pub Date : 2020-07-01
    Patrick Koopmann; Warren Del-Pinto; Sophie Tourret; Renate A. Schmidt

    Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocabulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. We present a method that performs signature-based abduction

    更新日期:2020-07-03
  • Minimal witnesses for probabilistic timed automata
    arXiv.cs.LO Pub Date : 2020-07-01
    Simon Jantsch; Florian Funke; Christel Baier

    Witnessing subsystems have proven to be a useful concept in the analysis of probabilistic systems, for example as diagnostic information on why a given property holds or as input to refinement algorithms. This paper introduces witnessing subsystems for reachability problems in probabilistic timed automata (PTA). Using a new operation on difference bounds matrices, it is shown how Farkas certificates

    更新日期:2020-07-02
  • Reasoning with Contextual Knowledge and Influence Diagrams
    arXiv.cs.LO Pub Date : 2020-07-01
    Erman Acar; Rafael Peñaloza

    Influence diagrams (IDs) are well-known formalisms extending Bayesian networks to model decision situations under uncertainty. Although they are convenient as a decision theoretic tool, their knowledge representation ability is limited in capturing other crucial notions such as logical consistency. We complement IDs with the light-weight description logic (DL) EL to overcome such limitations. We consider

    更新日期:2020-07-02
  • Decidable Entailments in Separation Logic with Inductive Definitions: Beyond Established Systems
    arXiv.cs.LO Pub Date : 2020-07-01
    Mnacho Echenim; Radu Iosif; Nicolas Peltier

    We define a class of Separation Logic formulae, whose entailment problem: given formulae $\phi, \psi_1, \ldots, \psi_n$, is every model of $\phi$ a model of some $\psi_i$? is 2EXPTIME-complete. The formulae in this class are existentially quantified separating conjunctions involving predicate atoms, interpreted by the least sets of store-heap structures that satisfy a set of inductive rules, which

    更新日期:2020-07-02
  • A Typo in the Paterson-Wegman-de Champeaux algorithm
    arXiv.cs.LO Pub Date : 2020-07-01
    Valeriu Motroi; Stefan Ciobaca

    We investigate the Paterson-Wegman-de Champeaux linear-time unification algorithm. We show that there is a small mistake in the de Champeaux presentation of the algorithm and we provide a fix.

    更新日期:2020-07-02
  • The Integers as a Higher Inductive Type
    arXiv.cs.LO Pub Date : 2020-07-01
    Thorsten Altenkirch; Luis Scoccola

    We consider the problem of defining the integers in Homotopy Type Theory (HoTT). We can define the type of integers as signed natural numbers (i.e., using a coproduct), but its induction principle is very inconvenient to work with, since it leads to an explosion of cases. An alternative is to use set-quotients, but here we need to use set-truncation to avoid non-trivial higher equalities. This results

    更新日期:2020-07-02
  • Cartesian closed bicategories: type theory and coherence
    arXiv.cs.LO Pub Date : 2020-07-01
    Philip Saville

    In this thesis I lift the Curry--Howard--Lambek correspondence between the simply-typed lambda calculus and cartesian closed categories to the bicategorical setting, then use the resulting type theory to prove a coherence result for cartesian closed bicategories. Cartesian closed bicategories---2-categories `up to isomorphism' equipped with similarly weak products and exponentials---arise in logic

    更新日期:2020-07-02
  • Computation of the Transient in Max-Plus Linear Systems via SMT-Solving
    arXiv.cs.LO Pub Date : 2020-07-01
    Alessandro Abate; Alessandro Cimatti; Andrea Micheli; Muhammad Syifa'ul Mufid

    This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art techniques, our approach allows the analysis of periodic behaviors for subsets of initial states, as well as the characterization of sets of initial states exhibiting

    更新日期:2020-07-02
  • Situation Calculus by Term Rewriting
    arXiv.cs.LO Pub Date : 2020-06-30
    David A. Plaisted

    A version of the situation calculus in which situations are represented as first-order terms is presented. Fluents can be computed from the term structure, and actions on the situations correspond to rewrite rules on the terms. Actions that only depend on or influence a subset of the fluents can be described as rewrite rules that operate on subterms of the terms in some cases. If actions are bidirectional

    更新日期:2020-07-02
  • An Approach to Regular Separability in Vector Addition Systems
    arXiv.cs.LO Pub Date : 2020-06-30
    Wojciech Czerwiński; Georg Zetzsche

    We study the problem of regular separability of languages of vector addition systems with states (VASS). It asks whether for two given VASS languages K and L, there exists a regular language R that includes K and is disjoint from L. While decidability of the problem in full generality remains an open question, there are several subclasses for which decidability has been shown: It is decidable for (i)

    更新日期:2020-07-02
  • Verification of indefinite-horizon POMDPs
    arXiv.cs.LO Pub Date : 2020-06-30
    Alexander Bork; Sebastian Junges; Joost-Pieter Katoen; Tim Quatmann

    The verification problem in MDPs asks whether, for any policy resolving the nondeterminism, the probability that something bad happens is bounded by some given threshold. This verification problem is often overly pessimistic, as the policies it considers may depend on the complete system state. This paper considers the verification problem for partially observable MDPs, in which the policies make their

    更新日期:2020-07-02
  • Algebraic models of simple type theories: a polynomial approach
    arXiv.cs.LO Pub Date : 2020-06-30
    Nathanael Arkor; Marcelo Fiore

    We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed $\lambda$-calculi, the computational $\lambda$-calculus, and predicate logic. Simple type theories are given models in presheaf categories, with structure specified

    更新日期:2020-07-01
  • It's Time to Play Safe: Shield Synthesis for Timed Systems
    arXiv.cs.LO Pub Date : 2020-06-30
    Roderick Bloem; Peter Gjøl Jensen; Bettina Könighofer; Kim Guldstrand Larsen; Florian Lorber; Alexander Palmisano

    Erroneous behaviour in safety critical real-time systems may inflict serious consequences. In this paper, we show how to synthesize timed shields from timed safety properties given as timed automata. A timed shield enforces the safety of a running system while interfering with the system as little as possible. We present timed post-shields and timed pre-shields. A timed pre-shield is placed before

    更新日期:2020-07-01
  • Neural Datalog Through Time: Informed Temporal Modeling via Logical Specification
    arXiv.cs.LO Pub Date : 2020-06-30
    Hongyuan Mei; Guanghui Qin; Minjie Xu; Jason Eisner

    Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of how past events might affect an event's present probability, we propose using a temporal deductive database to track structured facts over time. Rules serve to

    更新日期:2020-07-01
  • Frege's theory of types
    arXiv.cs.LO Pub Date : 2020-06-30
    Bruno Bentzen

    There is a widespread assumption in type theory that the discipline begins with Russell's efforts to resolve paradoxes concerning the naive notion of a class. My aim in this paper is to argue that Frege's sharp distinction between terms denoting objects and terms denoting functions on the basis of their saturation anticipate a simple type theory, although Frege vacillates between regarding functions

    更新日期:2020-07-01
  • Sense, reference, and computation
    arXiv.cs.LO Pub Date : 2020-06-30
    Bruno Bentzen

    In this paper, I revisit Frege's theory of sense and reference in the constructive setting of the meaning explanations of type theory, extending and sharpening a program--value analysis of sense and reference proposed by Martin-L\"of building on previous work of Dummett. I propose a computational identity criterion for senses and argue that it validates what I see as the most plausible interpretation

    更新日期:2020-07-01
  • Algebraic coherent confluence and higher-dimensional globular Kleene algebras
    arXiv.cs.LO Pub Date : 2020-06-29
    Cameron Calk; Eric Goubault; Philippe Malbos; Georg Struth

    We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent proofs by confluence. To this end, we introduce the structure of modal higher-dimensional globular Kleene algebra, a higher-dimensional generalisation of modal and concurrent Kleene algebra. We give a calculation of a coherent Church-Rosser theorem and Newman's lemma in higher-dimensional Kleene algebras

    更新日期:2020-06-30
  • Game Comonads & Generalised Quantifiers
    arXiv.cs.LO Pub Date : 2020-06-29
    Adam Ó Conghaile; Anuj Dawar

    Game comonads, introduced by Abramsky, Dawar and Wang and developed by Abramsky and Shah, give an interesting categorical semantics to some Spoiler-Duplicator games that are common in finite model theory. In particular they expose connections between one-sided and two-sided games, and parameters such as treewidth and treedepth and corresponding notions of decomposition. In the present paper, we expand

    更新日期:2020-06-30
  • Access-based Intuitionistic Knowledge
    arXiv.cs.LO Pub Date : 2020-06-29
    Steffen Lewitzka

    We introduce the concept of access-based intuitionistic knowledge which relies on the intuition that agent $i$ knows $\varphi$ if $i$ has found access to a proof of $\varphi$. Basic principles are distribution and factivity of knowledge as well as $\square\varphi\rightarrow K_i\varphi$ and $K_i(\varphi\vee\psi) \rightarrow (K_i\varphi\vee K_i\psi)$, where $\square\varphi$ reads `$\varphi$ is proved'

    更新日期:2020-06-30
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