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  • Cartesian Difference Categories
    arXiv.cs.LO Pub Date : 2020-11-25
    Mario Alvarez-Picallo; Jean-Simon Pacaud Lemay

    Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential categories include classical differential calculus of smooth functions and categorical models of the differential $\lambda$-calculus. However, Cartesian differential categories cannot account for other interesting notions of

    更新日期:2020-11-27
  • New method of verifying cryptographic protocols based on the process model
    arXiv.cs.LO Pub Date : 2020-11-24
    A. M. Mironov

    A cryptographic protocol (CP) is a distributed algorithm designed to provide a secure communication in an insecure environment. CPs are used, for example, in electronic payments, electronic voting procedures, database access systems, etc. Errors in the CPs can lead to great financial and social damage, therefore it is necessary to use mathematical methods to justify the correctness and safety of the

    更新日期:2020-11-25
  • Provably-Robust Runtime Monitoring of Neuron Activation Patterns
    arXiv.cs.LO Pub Date : 2020-11-24
    Chih-Hong Cheng

    For deep neural networks (DNNs) to be used in safety-critical autonomous driving tasks, it is desirable to monitor in operation time if the input for the DNN is similar to the data used in DNN training. While recent results in monitoring DNN activation patterns provide a sound guarantee due to building an abstraction out of the training data set, reducing false positives due to slight input perturbation

    更新日期:2020-11-25
  • The Reads-From Equivalence for the TSO and PSO Memory Models
    arXiv.cs.LO Pub Date : 2020-11-23
    Truc Lam Bui; Krishnendu Chatterjee; Tushar Gautam; Andreas Pavlogiannis; Viktor Toman

    The verification of concurrent programs remains an open challenge due to the non-determinism in inter-process communication. Instead of exploring concrete executions, stateless model-checking (SMC) techniques partition the execution space into equivalence classes, and explore each class as opposed to each execution. For the relaxed memory models of TSO and PSO (total/partial store order), the standard

    更新日期:2020-11-25
  • Diagrammatic Design and Study of Ansätze for Quantum Machine Learning
    arXiv.cs.LO Pub Date : 2020-11-22
    Richie Yeung

    Given the rising popularity of quantum machine learning (QML), it is important to develop techniques that effectively simplify commonly adopted families of parameterised quantum circuits (commonly known as ans\"{a}tze). This thesis pioneers the use of diagrammatic techniques to reason with QML ans\"{a}tze. We take commonly used QML ans\"{a}tze and convert them to diagrammatic form and give a full description

    更新日期:2020-11-25
  • Towards Abstract Relational Learning in Human Robot Interaction
    arXiv.cs.LO Pub Date : 2020-11-20
    Mohamadreza Faridghasemnia; Daniele Nardi; Alessandro Saffiotti

    Humans have a rich representation of the entities in their environment. Entities are described by their attributes, and entities that share attributes are often semantically related. For example, if two books have "Natural Language Processing" as the value of their `title' attribute, we can expect that their `topic' attribute will also be equal, namely, "NLP". Humans tend to generalize such observations

    更新日期:2020-11-23
  • Categorical models of Linear Logic with fixed points of formulas
    arXiv.cs.LO Pub Date : 2020-11-19
    Thomas EhrhardIRIF; Farzad JafarrahmaniIRIF

    We develop a denotational semantics of Linear Logic with least and greatest fixed points in a general categorical setting based on the notion of Seely category and on strong functors acting on them. We exhibit a simple instance of this setting in the category of sets and relations, where least and greatest fixed points are interpreted in the same way, and in a category of sets equipped with a notion

    更新日期:2020-11-23
  • An algebraic study of the first order version of some implicational fragments of the three-valued Lukasiewicz logic
    arXiv.cs.LO Pub Date : 2020-10-23
    Aldo Figallo-Orellano; Juan Sebastian Slagter

    MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a fragment of trivalent Lukasiewicz logic is studied. The propositional and first-order logic is presented. The maximal consistent theories are studied as Monteiro's maximal

    更新日期:2020-11-21
  • Logics with Multiteam Semantics
    arXiv.cs.LO Pub Date : 2020-11-19
    Erich Grädel; Richard Wilke

    Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such assignments, called a team. Team semantics is appropriate for a purely logical understanding of dependency notions, where only the presence or absence of data matters

    更新日期:2020-11-21
  • Learning Languages with Decidable Hypotheses
    arXiv.cs.LO Pub Date : 2020-10-15
    Julian Berger; Maximilian Böther; Vanja Doskoč; Jonathan Gadea Harder; Nicolas Klodt; Timo Kötzing; Winfried Lötzsch; Jannik Peters; Leon Schiller; Lars Seifert; Armin Wells; Simon Wietheger

    In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language. This so-called $W$-index allows for naming arbitrary computably enumerable languages, with the drawback that even the membership problem is undecidable. In this paper we use a different system which allows for naming arbitrary decidable languages, namely programs for characteristic functions

    更新日期:2020-11-21
  • Efficient Full Higher-Order Unification
    arXiv.cs.LO Pub Date : 2020-11-18
    Petar Vukmirović; Alexander Bentkamp; Visa Nummelin

    We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set of unifiers. We identify a new such fragment and describe a procedure for computing its unifiers. Our

    更新日期:2020-11-21
  • Generic Ontology Design Patterns: Roles and Change over Time
    arXiv.cs.LO Pub Date : 2020-11-18
    Bernd Krieg-Brückner; Till Mossakowski; Mihai Codescu

    In this chapter we propose Generic Ontology Design Patterns, GODPs, as a methodology for representing and instantiating ontology design patterns in a way that is adaptable, and allows domain experts (and other users) to safely use them without cluttering their ontologies.

    更新日期:2020-11-19
  • Mixed Nondeterministic-Probabilistic Interfaces
    arXiv.cs.LO Pub Date : 2020-11-05
    Albert BenvenisteHYCOMES; Kim LarsenIRIT; Jean-Baptiste RacletIRIT

    Interface theories are powerful frameworks supporting incremental and compositional design of systems through refinements and constructs for conjunction, and parallel composition. In this report we present a first Interface Theor -- |Modal Mixed Interfaces -- for systems exhibiting both non-determinism and randomness in their behaviour. The associated component model -- Mixed Markov Decision Processes

    更新日期:2020-11-19
  • Answering Regular Path Queries Over SQ Ontologies
    arXiv.cs.LO Pub Date : 2020-11-17
    Víctor Gutiérrez-Basulto; Yazmín Ibáñez-García; Jean Christoph Jung

    We study query answering in the description logic $\mathcal{SQ}$ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for $\mathcal{SQ}$ knowledge bases and, building upon this, an optimal automata-based algorithm for answering positive existential regular path queries in 2ExpTime.

    更新日期:2020-11-18
  • Revising the classic computing paradigm and its technological implementations
    arXiv.cs.LO Pub Date : 2020-11-16
    János Végh

    Today's computing is told to be based on the classic paradigm, proposed by von Neumann, a three-quarter century ago. However, that paradigm was justified (for the timing relations of) vacuum tubes only. The technological development invalidated the classic paradigm (but not the model!) and led to catastrophic performance losses in computing systems, from operating gate level to large networks, including

    更新日期:2020-11-18
  • Declarative Approaches to Counterfactual Explanations for Classification
    arXiv.cs.LO Pub Date : 2020-11-15
    Leopoldo Bertossi

    We propose answer-set programs that specify and compute counterfactual interventions as a basis for causality-based explanations to the outcomes from classification models. They can be applied with black-box models, and also with models that can be specified as logic programs, such as rule-based classifiers. The main focus is on the specification and computation of maximum-responsibility counterfactual

    更新日期:2020-11-17
  • Reachability in two-parametric timed automata with one parameter is EXPSPACE-complete
    arXiv.cs.LO Pub Date : 2020-11-13
    Stefan Göller; Mathieu Hilaire

    Parametric timed automata (PTA) are an extension of timed automata in which clocks can be compared against parameters. The reachability problem asks for the existence of an assignment of the parameters to the non-negative integers such that reachability holds in the underlying timed automaton. The reachability problem for PTA is long known to be undecidable, already over three parametric clocks. A

    更新日期:2020-11-17
  • Functorial Semantics for Partial Theories
    arXiv.cs.LO Pub Date : 2020-11-12
    Ivan Di Liberti; Fosco Loregian; Chad Nester; Paweł Sobociński

    We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of string diagrams as terms. This allows for equational reasoning about the class of models defined by a partial theory. We demonstrate the expressivity of such equational

    更新日期:2020-11-16
  • Randomized fast no-loss expert system to play tic tac toe like a human
    arXiv.cs.LO Pub Date : 2020-09-23
    Aditya Jyoti Paul

    This paper introduces a blazingly fast, no-loss expert system for Tic Tac Toe using Decision Trees called T3DT, that tries to emulate human gameplay as closely as possible. It does not make use of any brute force, minimax or evolutionary techniques, but is still always unbeatable. In order to make the gameplay more human-like, randomization is prioritized and T3DT randomly chooses one of the multiple

    更新日期:2020-11-16
  • Session Coalgebras: A Coalgebraic View on Session Types and Communication Protocols
    arXiv.cs.LO Pub Date : 2020-11-11
    Alex C. Keizer; Henning Basold; Jorge A. Pérez

    Compositional methods are central to the development and verification of software systems. They allow to break down large systems into smaller components, while enabling reasoning about the behaviour of the composed system. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types

    更新日期:2020-11-12
  • Crime Prediction Using Multiple-ANFIS Architecture and Spatiotemporal Data
    arXiv.cs.LO Pub Date : 2020-11-07
    Mashnoon Islam; Redwanul Karim; Kalyan Roy; Saif Mahmood; Sadat Hossain; M. Rashedur Rahman

    Statistical values alone cannot bring the whole scenario of crime occurrences in the city of Dhaka. We need a better way to use these statistical values to predict crime occurrences and make the city a safer place to live. Proper decision-making for the future is key in reducing the rate of criminal offenses in an area or a city. If the law enforcement bodies can allocate their resources efficiently

    更新日期:2020-11-12
  • A translation of weighted LTL formulas to weighted Büchi automata over ω-valuation monoids
    arXiv.cs.LO Pub Date : 2020-11-10
    Eleni Mandrali

    In this paper we introduce a weighted LTL over product {\omega}-valuation monoids that satisfy specific properties. We also introduce weighted generalized B\"uchi automata with {\epsilon}-transitions, as well as weighted B\"uchi automata with {\epsilon}-transitions over product {\omega}-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted B\"uchi

    更新日期:2020-11-12
  • Domain Semirings United
    arXiv.cs.LO Pub Date : 2020-11-09
    Uli Fahrenberg; Christian Johansen; Georg Struth; Krzysztof Ziemiánksi

    Domain operations on semirings have been axiomatised in two different ways: by a map from an additively idempotent semiring into a boolean subalgebra of the semiring bounded by the additive and multiplicative unit of the semiring, or by an endofunction on a semiring that induces a distributive lattice bounded by the two units as its image. This note presents classes of semirings where these approaches

    更新日期:2020-11-12
  • Curious properties of latency distributions
    arXiv.cs.LO Pub Date : 2020-11-05
    Michał J. Gajda

    Network latency distributions, their algebra, and use examples. This paper considers modeling of capacity-insensitive processes and distributed systems. It provides algebraic properties of the latency distribution algebra and Haskell code to implement the model.

    更新日期:2020-11-12
  • A Syntactic Approach to Studying Strongly Equivalent Logic Programs
    arXiv.cs.LO Pub Date : 2020-11-09
    Bin Wang; Runqiu Hu; Shutao Zhang; Zhizheng Zhang

    In the field of Answer Set Programming (ASP), two logic programs are strongly equivalent if they are ordinarily equivalent under any extensions. This property provides a theoretical foundation for studying many aspects of logic programs such as program simplification and transformation etc. Therefore, strong equivalence has been investigated extensively for ASP and its extensions such as LPMLN. In

    更新日期:2020-11-12
  • Contextuality: At the Borders of Paradox
    arXiv.cs.LO Pub Date : 2020-11-07
    Samson Abramsky

    Contextuality is a key feature of quantum mechanics. We present the sheaf-theoretic approach to contextuality introduced by Abramsky and Brandenburger, and show how it covers a range of logical and physical phenomena "at the borders of paradox".

    更新日期:2020-11-12
  • Generating Concurrent Programs From Sequential Data Structure Knowledge
    arXiv.cs.LO Pub Date : 2020-11-08
    Sarat Chandra Varanasi; Neeraj Mittal; Gopal Gupta

    In this paper we tackle the problem of automatically designing concurrent data structure operations given a sequential data structure specification and knowledge about concurrent behavior. Designing concurrent code is a non-trivial task even in simplest of cases. Humans often design concurrent data structure operations by transforming sequential versions into their respective concurrent versions. This

    更新日期:2020-11-12
  • Smooth approximations and CSPs over finitely bounded homogeneous structures
    arXiv.cs.LO Pub Date : 2020-11-08
    Antoine Mottet; Michael Pinsker

    We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the order of the rationals. Apart from obtaining these dichotomy results, we show how our new proof technique allows to unify and significantly simplify the previous

    更新日期:2020-11-12
  • A graded dependent type system with a usage-aware semantics (extended version)
    arXiv.cs.LO Pub Date : 2020-11-08
    Pritam Choudhury; Harley Eades III; Richard A. Eisenberg; Stephanie C Weirich

    Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop a novel version of such a graded dependent type system, including functions, tensor products, additive sums, and a unit type. Since standard operational semantics is resource-agnostic, we develop a heap-based operational semantics and prove a soundness theorem that shows correct

    更新日期:2020-11-12
  • Reasoning about Temporary Coalitions and LTL-definable Ordered Objectives in Infinite Concurrent Multiplayer Games
    arXiv.cs.LO Pub Date : 2020-11-07
    Dimitar P. Guelev

    We propose enhancing the use of propositions for denoting decisions and strategies as established in temporal languages such as CTL*, if interpreted on concurrent game models. The enhancement enables specifying varying coalition structure. In quantified CTL* this technique also enables quantifying over coalition structure, and we use it to quantify over an extended form of strategy profiles which capture

    更新日期:2020-11-12
  • On the Complexity of CSP-based Ideal Membership Problems
    arXiv.cs.LO Pub Date : 2020-11-07
    Andrei A. Bulatov; Akbar Rafiey

    In this paper we consider the Ideal Membership Problem (IMP for short), in which we are given real polynomials $f_0, f_1, \dots, f_k$ and the question is to decide whether $f_0$ belongs to the ideal generated by $f_1, \dots, f_k$. In the more stringent version the task is also to find a proof of this fact. The IMP underlies many proof systems based on polynomials such as Nullstellensatz, Polynomial

    更新日期:2020-11-12
  • Extending Equational Monadic Reasoning with Monad Transformers
    arXiv.cs.LO Pub Date : 2020-11-06
    Reynald Affeldt; David Nowak

    There is a recent interest for the verification of monadic programs using proof assistants. This line of research raises the question of the integration of monad transformers, a standard technique to combine monads. In this paper, we extend Monae, a Coq library for monadic equational reasoning, with monad transformers and we explain the benefits of this extension. Our starting point is the existing

    更新日期:2020-11-09
  • Automatic Differentiation in PCF
    arXiv.cs.LO Pub Date : 2020-11-06
    Damiano Mazza; Michele Pagani

    We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive functions included in the language, AD is almost everywhere correct, that is, it computes the derivative or gradient of the program under consideration except for

    更新日期:2020-11-09
  • Learning with Molecules beyond Graph Neural Networks
    arXiv.cs.LO Pub Date : 2020-11-06
    Gustav Sourek; Filip Zelezny; Ondrej Kuzelka

    We demonstrate a deep learning framework which is inherently based in the highly expressive language of relational logic, enabling to, among other things, capture arbitrarily complex graph structures. We show how Graph Neural Networks and similar models can be easily covered in the framework by specifying the underlying propagation rules in the relational logic. The declarative nature of the used language

    更新日期:2020-11-09
  • Iterated multiplication in $VTC^0$
    arXiv.cs.LO Pub Date : 2020-11-05
    Emil Jeřábek

    We show that $VTC^0$, the basic theory of bounded arithmetic corresponding to the complexity class $\mathrm{TC}^0$, proves the $IMUL$ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the $\mathrm{TC}^0$ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, $VTC^0$ can also prove the integer

    更新日期:2020-11-09
  • Complex Query Answering with Neural Link Predictors
    arXiv.cs.LO Pub Date : 2020-11-06
    Erik Arakelyan; Daniel Daza; Pasquale Minervini; Michael Cochez

    Neural link predictors are immensely useful for identifying missing edges in large scale Knowledge Graphs. However, it is still not clear how to use these models for answering more complex queries that arise in a number of domains, such as queries using logical conjunctions, disjunctions, and existential quantifiers, while accounting for missing edges. In this work, we propose a framework for efficiently

    更新日期:2020-11-09
  • Secure Information Flow Connections
    arXiv.cs.LO Pub Date : 2020-11-05
    Chandrika Bhardwaj; Sanjiva Prasad

    Denning's lattice model provided secure information flow analyses with an intuitive mathematical foundation: the lattice ordering determines permitted flows. We examine how this framework may be extended to support the flow of information between autonomous organisations, each employing possibly quite different security lattices and information flow policies. We propose a connection framework that

    更新日期:2020-11-09
  • Towards a more perfect union type
    arXiv.cs.LO Pub Date : 2020-11-05
    Michał J. Gajda

    We present a principled theoretical framework for inferring and checking the union types, and show its work in practice on JSON data structures. The framework poses a union type inference as a learning problem from multiple examples. The categorical framework is generic and easily extensible.

    更新日期:2020-11-09
  • The logic of contextuality
    arXiv.cs.LO Pub Date : 2020-11-05
    Samson Abramsky; Rui Soares Barbosa

    Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality from a structural point of view, in the setting of partial Boolean algebras introduced by Kochen and Specker in their seminal work. These contrast with traditional

    更新日期:2020-11-09
  • MSO Undecidability for some Hereditary Classes of Unbounded Clique-Width
    arXiv.cs.LO Pub Date : 2020-11-05
    Anuj Dawar; Abhisekh Sankaran

    Seese's conjecture for finite graphs states that monadic second-order logic (MSO) is undecidable on all graph classes of unbounded clique-width. We show that to establish this it would suffice to show that grids of unbounded size can be interpreted in two families of graph classes: minimal hereditary classes of unbounded clique-width; and antichains of unbounded clique-width under the induced subgraph

    更新日期:2020-11-06
  • Monadic second-order logic and the domino problem on self-similar graphs
    arXiv.cs.LO Pub Date : 2020-11-05
    Laurent Bartholdi

    We consider the domino problem on Schreier graphs of self-similar groups, and more generally their monadic second-order logic. On the one hand, we prove that if the group is bounded then the graph's monadic second-order logic is decidable. This covers, for example, the Sierpi\'nski gasket graphs and the Schreier graphs of the Basilica group. On the other hand, we already prove undecidability of the

    更新日期:2020-11-06
  • Necessary and Sufficient Explanations in Abstract Argumentation
    arXiv.cs.LO Pub Date : 2020-11-04
    AnneMarie Borg; Floris Bex

    In this paper, we discuss necessary and sufficient explanations for formal argumentation - the question whether and why a certain argument can be accepted (or not) under various extension-based semantics. Given a framework with which explanations for argumentation-based conclusions can be derived, we study necessity and sufficiency: what (sets of) arguments are necessary or sufficient for the (non-)acceptance

    更新日期:2020-11-05
  • Probabilistic Bisimulation for Parameterized Systems (Technical Report)
    arXiv.cs.LO Pub Date : 2020-11-04
    Chih-Duo Hong; Anthony W. Lin; Rupak Majumdar; Philipp Rümmer

    Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot of work on verifying probabilistic bisimulation for finite systems. This is however not the case for parameterized systems, where the problem is in general undecidable

    更新日期:2020-11-05
  • Out of Control: Reducing Probabilistic Models by Control-State Elimination
    arXiv.cs.LO Pub Date : 2020-11-02
    Tobias Winkler; Johannes Lehman; Joost-Pieter Katoen

    We present a new, simple technique to reduce state space sizes in probabilistic model checking when the input model is defined in a programming formalism like the PRISM modeling language. Similar in spirit to traditional compiler optimizations that try to summarize instruction sequences into shorter ones, our approach aims at computing the summary behavior of adjacent locations in the program's control-flow

    更新日期:2020-11-03
  • Partial Functions and Recursion in Univalent Type Theory
    arXiv.cs.LO Pub Date : 2020-10-31
    Cory Knapp

    We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability theory. We begin with a treatment of partial functions, using the notion of dominance, which is used in synthetic domain theory to discuss classes of partial maps

    更新日期:2020-11-03
  • How Testable is Business Software?
    arXiv.cs.LO Pub Date : 2020-11-01
    Peter Schrammel

    Most businesses rely on a significant stack of software to perform their daily operations. This software is business-critical as defects in this software have major impacts on revenue and customer satisfaction. The primary means for verification of this software is testing. We conducted an extensive analysis of Java software packages to evaluate their unit-testability. The results show that code in

    更新日期:2020-11-03
  • Towards making formal methods normal: meeting developers where they are
    arXiv.cs.LO Pub Date : 2020-10-30
    Alastair Reid; Luke Church; Shaked Flur; Sarah de Haas; Maritza Johnson; Ben Laurie

    Formal verification of software is a bit of a niche activity: it is only applied to the most safety-critical or security-critical software and it is typically only performed by specialized verification engineers. This paper considers whether it would be possible to increase adoption of formal methods by integrating formal methods with developers' existing practices and workflows. We do not believe

    更新日期:2020-11-02
  • Type safety of rewrite rules in dependent types
    arXiv.cs.LO Pub Date : 2020-10-30
    Frédéric BlanquiLSV,ENS Paris Saclay

    The expressiveness of dependent type theory can be extended by identifying types modulo some additional computation rules. But, for preserving the decidability of type-checking or the logical consistency of the system, one must make sure that those user-defined rewriting rules preserve typing. In this paper, we give a new method to check that property using Knuth-Bendix completion.

    更新日期:2020-11-02
  • Formalizing IMO Problems and Solutions in Isabelle/HOL
    arXiv.cs.LO Pub Date : 2020-10-30
    Filip MarićFaculty of Mathematics, University of Belgrade, Serbia; Sana Stojanović-{\Dj}urđevićFaculty of Mathematics, University of Belgrade, Serbia

    The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated, requires to build an AI that can win a gold medal in the competition. We present some initial steps that could help to tackle this goal by creating a public repository

    更新日期:2020-11-02
  • Isabelle/HOL as a Meta-Language for Teaching Logic
    arXiv.cs.LO Pub Date : 2020-10-30
    Asta Halkjær FromTechnical University of Denmark; Jørgen VilladsenTechnical University of Denmark; Patrick BlackburnRoskilde University

    Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of classical propositional logic with only two primitive symbols), the second is the Natural Deduction Assistant (NaDeA), and the third is a one-sided sequent calculus that

    更新日期:2020-11-02
  • Teaching Interactive Proofs to Mathematicians
    arXiv.cs.LO Pub Date : 2020-10-30
    Mauricio Ayala-RincónUniversidade de Brasília; Thaynara Arielly de LimaUniversidade Federal de Goiás

    This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools through short courses. In particular, it is discussed how, using as case-of-study algebraic notions and properties, the use of the proof assistant Prototype Verification

    更新日期:2020-11-02
  • String Constraints with Concatenation and Transducers Solved Efficiently (Technical Report)
    arXiv.cs.LO Pub Date : 2020-10-29
    Lukas Holik; Petr Janku; Anthony W. Lin; Philipp Rümmer; Tomas Vojnar

    String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of cross-site scripting (XSS). A popular string analysis technique includes symbolic executions, which at their core use string (constraint) solvers. Such solvers typically reason about constraints expressed in theories over strings with the concatenation

    更新日期:2020-11-02
  • Thinking About Causation: A Causal Language with Epistemic Operators
    arXiv.cs.LO Pub Date : 2020-10-30
    Fausto Barbero; Katrin Schulz; Sonja Smets; Fernando R. Velázquez-Quesada; Kaibo Xie

    This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the side of the object language, we add operators to express knowledge and the act of observing new information. We provide a sound and complete axiomatization of the

    更新日期:2020-11-02
  • Three computational models and its equivalence
    arXiv.cs.LO Pub Date : 2020-10-26
    Ciro Ivan Garcia Lopez

    The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, to the ones he asked, is to give a precise description of the notion of algorithm. In the search for a good definition arose three independent theories: Turing and the Turing machines, G\"odel and the recursive functions, Church and the Lambda Calculus. Later there were established by Kleene that

    更新日期:2020-10-30
  • Linearizing Combinators
    arXiv.cs.LO Pub Date : 2020-10-29
    Robin Cockett; Jean-Simon Pacaud Lemay

    In 2017, Bauer, Johnson, Osborne, Riehl, and Tebbe (BJORT) showed that the Abelian functor calculus provides an example of a Cartesian differential category. The definition of a Cartesian differential category is based on a differential combinator which directly formalizes the total derivative from multivariable calculus. However, in the aforementioned work the authors used techniques from Goodwillie's

    更新日期:2020-10-30
  • Verification of Patterns
    arXiv.cs.LO Pub Date : 2020-10-26
    Yong Wang

    The software patterns provide building blocks to the design and implementation of a software system, and try to make the software engineering to progress from experience to science. The software patterns were made famous because of the introduction as the design patterns. After that, patterns have been researched and developed widely and rapidly. The series of books of pattern-oriented software architecture

    更新日期:2020-10-30
  • Actris 2.0: Asynchronous Session-Type Based Reasoning in Separation Logic
    arXiv.cs.LO Pub Date : 2020-10-28
    Jonas Kastberg Hinrichsen; Jesper Bengtson; Robbert Krebbers

    Message passing is a useful abstraction for implementing concurrent programs. For real-world systems, however, it is often combined with other programming and concurrency paradigms, such as higher-order functions, mutable state, shared-memory concurrency, and locks. We present Actris: a logic for proving functional correctness of programs that use a combination of the aforementioned features. Actris

    更新日期:2020-10-30
  • A Cyclic Proof System for HFLN
    arXiv.cs.LO Pub Date : 2020-10-28
    Mayuko Kori; Takeshi Tsukada; Naoki Kobayashi

    A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the first cyclic proof system for a higher-order logic, to our knowledge. Due to the presence of higher-order predicates and alternating fixed-points, our cyclic proof

    更新日期:2020-10-30
  • Approximate Evaluation of First-Order Counting Queries
    arXiv.cs.LO Pub Date : 2020-10-28
    Jan Dreier; Peter Rossmanith

    Kuske and Schweikardt introduced the very expressive first-order counting logic FOC(P) to model database queries with counting operations. They showed that there is an efficient model-checking algorithm on graphs with bounded degree, while Grohe and Schweikardt showed that probably no such algorithm exists for trees of bounded depth. We analyze the fragment FO({>0}) of this logic. While we remove for

    更新日期:2020-10-30
  • Verifying Graph Programs with First-Order Logic (Extended Version)
    arXiv.cs.LO Pub Date : 2020-10-27
    Gia Wulandari; Detlef Plump

    We consider Hoare-style verification for the graph programming language GP 2. In previous work, graph properties were specified by so-called E-conditions which extend nested graph conditions. However, this type of assertions is not easy to comprehend by programmers that are used to formal specifications in standard first-order logic. In this paper, we present an approach to verify GP 2 programs with

    更新日期:2020-10-30
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