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  • 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
  • Extensive Infinite Games and Escalation, an exercise in Agda
    arXiv.cs.LO Pub Date : 2020-06-19
    Pierre LescanneLIP

    Escalation in games is when agents keep playing forever. Based on formal proofs we claim that if agents assume that resource are infinite, escalation is rational.

    更新日期:2020-06-29
  • Homotopy Theoretic and Categorical Models of Neural Information Networks
    arXiv.cs.LO Pub Date : 2020-06-23
    Yuri Manin; Matilde Marcolli

    In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial

    更新日期:2020-06-29
  • Generating induction principles and subterm relations for inductive types using MetaCoq
    arXiv.cs.LO Pub Date : 2020-06-25
    Bohdan Liesnikov; Marcel Ullrich; Yannick Forster

    We implement three Coq plugins regarding inductive types in MetaCoq. The first plugin is a simple syntax transformation generating alternative constructors for inductive types by abstracting over concrete indices in the types of the constructors. The second plugin re-implements Coq's $\texttt{Scheme Induction}$ command in MetaCoq, and extends it to nested inductive types, e.g. types like rose trees

    更新日期:2020-06-29
  • A Hennessy-Milner Theorem for ATL with Imperfect Information
    arXiv.cs.LO Pub Date : 2020-06-26
    Francesco Belardinelli; Catalin Dima; Vadim Malvone; Ferucio Tiplea

    We show that a history-based variant of alternating bisimulation with imperfect information allows it to be related to a variant of Alternating-time Temporal Logic (ATL) with imperfect information by a full Hennessy-Milner theorem. The variant of ATL we consider has a common knowledge semantics, which requires that the uniform strategy available for a coalition to accomplish some goal must be common

    更新日期:2020-06-29
  • Distributed Policy Synthesis of Multi-Agent Systems With Graph Temporal Logic Specifications
    arXiv.cs.LO Pub Date : 2020-06-25
    Murat Cubuktepe; Zhe Xu; Ufuk Topcu

    We study the distributed synthesis of policies for multi-agent systems to perform spatial-temporal tasks. We formalize the synthesis problem as a factored Markov decision process subject to graph temporal logic specifications. The transition function and task of each agent is a function of the agent itself and its neighboring agents. By leveraging the structure in the model, and the specifications

    更新日期:2020-06-29
  • DeepAbstract: Neural Network Abstraction for Accelerating Verification
    arXiv.cs.LO Pub Date : 2020-06-24
    Pranav Ashok; Vahid Hashemi; Jan Křetínský; Stefanie Mohr

    While abstraction is a classic tool of verification to scale it up, it is not used very often for verifying neural networks. However, it can help with the still open task of scaling existing algorithms to state-of-the-art network architectures. We introduce an abstraction framework applicable to fully-connected feed-forward neural networks based on clustering of neurons that behave similarly on some

    更新日期:2020-06-25
  • ReLoC Reloaded: A Mechanized Relational Logic for Fine-Grained Concurrency and Logical Atomicity
    arXiv.cs.LO Pub Date : 2020-06-24
    Dan Frumin; Robbert Krebbers; Lars Birkedal

    We present a new version of ReLoC: a relational logic for proving refinements of programs in a language with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of ReLoC is the refinement judgment $e \precsim e' : \tau$, which expresses that a program $e$ refines a program $e'$ at type $\tau$. In contrast to earlier work on refinements for languages with higher-order

    更新日期:2020-06-25
  • Formalizing the Soundness of the Encoding Methods of SAT-based Model Checking
    arXiv.cs.LO Pub Date : 2020-06-24
    Daisuke Ishii; Saito Fujii

    One of the effective model checking methods is to utilize the efficient decision procedure of SAT (or SMT) solvers. In a SAT-based model checking, a system and its property are encoded into a set of logic formulas and the safety is checked based on the satisfiability of the formulas. As the encoding methods are improved and crafted (e.g., k-induction and IC3/PDR), verifying their correctness becomes

    更新日期:2020-06-25
  • A Constructive, Type-Theoretic Approach to Regression via Global Optimisation
    arXiv.cs.LO Pub Date : 2020-06-23
    Dan R. Ghica; Todd Waugh Ambridge

    We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We see how the property of convergence of global optimisation is a straightforward consequence of searchability. The abstract setting allows us to generalise searchability

    更新日期:2020-06-24
  • Logical Neural Networks
    arXiv.cs.LO Pub Date : 2020-06-23
    Ryan Riegel; Alexander Gray; Francois Luus; Naweed Khan; Ndivhuwo Makondo; Ismail Yunus Akhalwaya; Haifeng Qian; Ronald Fagin; Francisco Barahona; Udit Sharma; Shajith Ikbal; Hima Karanam; Sumit Neelam; Ankita Likhyani; Santosh Srivastava

    We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning

    更新日期:2020-06-24
  • Encoding Legal Balancing: Automating an Abstract Ethico-Legal Value Ontology in Preference Logic
    arXiv.cs.LO Pub Date : 2020-06-23
    Christoph Benzmüller; David Fuenmayor; Bertram Lomfeld

    Enabling machines to legal balancing is a non-trivial task challenged by a multitude of factors some of which are addressed and explored in this work. We propose a holistic approach to formal modeling at different abstraction layers supported by a pluralistic framework in which the encoding of an ethico-legal value and upper ontology is developed in combination with the exploration of a formalization

    更新日期:2020-06-24
  • Expressive Logics for Coinductive Predicates
    arXiv.cs.LO Pub Date : 2020-06-22
    Clemens Kupke; Jurriaan Rot

    The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive

    更新日期:2020-06-23
  • Large and Infinitary Quotient Inductive-Inductive Types
    arXiv.cs.LO Pub Date : 2020-06-21
    András Kovács; Ambrus Kaposi

    Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors. QIITs are especially useful for algebraic descriptions of type theories and constructive definitions of real, ordinal and surreal numbers. We develop new metatheory for large QIITs, large elimination, recursive equations

    更新日期:2020-06-23
  • Graphs of relational structures: restricted types
    arXiv.cs.LO Pub Date : 2020-06-21
    Andrei A. Bulatov

    The algebraic approach to the Constraint Satisfaction Problem (CSP) uses high order symmetries of relational structures -- polymorphisms -- to study the complexity of the CSP. In this paper we further develop one of the methods the algebraic approach can be implemented, and apply it to some kinds of the CSP. This method was introduced in our LICS 2004 paper and involves the study of the local structure

    更新日期:2020-06-23
  • Moore's Paradox and the logic of belief
    arXiv.cs.LO Pub Date : 2020-06-19
    Andrés Páez

    Moores Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikkas interpretation of one of the doxastic operators is philosophically problematic and

    更新日期:2020-06-23
  • Learning to Prove from Synthetic Theorems
    arXiv.cs.LO Pub Date : 2020-06-19
    Eser Aygün; Zafarali Ahmed; Ankit Anand; Vlad Firoiu; Xavier Glorot; Laurent Orseau; Doina Precup; Shibl Mourad

    A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies on training with synthetic theorems, generated from a set of axioms. We show that such theorems can be used to train an automated prover and that the learned prover

    更新日期:2020-06-22
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