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A Conjecture for ATP Research arXiv.cs.LO Pub Date : 2024-03-15 Wolfgang Bibel
This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.
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Scaling Game-Theoretic Security Reasoning arXiv.cs.LO Pub Date : 2024-03-15 Sophie Rain, Lea Salome Brugger, Anja Petkovic Komel, Laura Kovacs, Michael Rawson
We present the CheckMate tool for automated verification of game-theoretic security properties, with application to blockchain protocols. CheckMate applies automated reasoning techniques to determine whether a game-theoretic protocol model is game-theoretically secure, that is, Byzantine fault tolerant and incentive compatible. We describe CheckMate's input format and its various components, modes
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Timed Strategies for Real-Time Rewrite Theories arXiv.cs.LO Pub Date : 2024-03-13 Carlos Olarte, Peter Csaba Ölveczky
In this paper we propose a language for conveniently defining a wide range of execution strategies for real-time rewrite theories, and provide Maude-strategy-implemented versions of most Real-Time Maude analysis methods, albeit with user-defined discrete and timed strategies. We also identify a new time sampling strategy that should provide both efficient and exhaustive analysis for many distributed
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Expiring opacity problems in parametric timed automata arXiv.cs.LO Pub Date : 2024-03-12 Étienne André, Engel Lefaucheux, Dylan Marinho
Information leakage can have dramatic consequences on the security of real-time systems. Timing leaks occur when an attacker is able to infer private behavior depending on timing information. In this work, we propose a definition of expiring timed opacity w.r.t. execution time, where a system is opaque whenever the attacker is unable to deduce the reachability of some private state solely based on
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Perennial Semantic Data Terms of Use for Decentralized Web arXiv.cs.LO Pub Date : 2024-03-12 Rui Zhao, Jun Zhao
In today's digital landscape, the Web has become increasingly centralized, raising concerns about user privacy violations. Decentralized Web architectures, such as Solid, offer a promising solution by empowering users with better control over their data in their personal `Pods'. However, a significant challenge remains: users must navigate numerous applications to decide which application can be trusted
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Local Intuitionistic Modal Logics and Their Calculi arXiv.cs.LO Pub Date : 2024-03-11 Philippe Balbiani, Han Gao, Çiğdem Gencer, Nicola Olivetti
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. We propose bi-nested calculi for LIK and these extensions, thus providing both a decision procedure and a procedure of finite
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Multiple Reachability in Linear Dynamical Systems arXiv.cs.LO Pub Date : 2024-03-11 Toghrul Karimov, Edon Kelmendi, Joël Ouaknine, James Worrell
We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly applying the linear map, enters the target set. When the source and target sets are semialgebraic, this problem can be reduced to a point-to-polytope reachability
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Local Computing By Partial Quantifier Elimination arXiv.cs.LO Pub Date : 2024-03-09 Eugene Goldberg
Localization of computations plays a crucial role in solving hard problems efficiently. We will refer to the techniques implementing such localization as ${\mathit local}$ ${\mathit computing}$. We relate local computing with $\mathit{partial}$ $\mathit{quantifier}$ $\mathit{elimination}$ (PQE). The latter is a generalization of regular quantifier elimination where one can take a $\mathit{part}$ of
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The interdefinability of expansions of Belnap-Dunn logic arXiv.cs.LO Pub Date : 2024-03-07 C. A. Middelburg
Belnap-Dunn logic, also knows as the logic of First-Degree Entailment, is a logic that can serve as the underlying logic of theories that are inconsistent or incomplete. For various reasons, different expansions of Belnap-Dunn logic with non-classical connectives have been studied. This paper investigates the question whether those expansions are interdefinable with an expansion whose connectives include
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Bridging Computational Notions of Depth arXiv.cs.LO Pub Date : 2024-03-06 Laurent Bienvenu, Christopher P. Porter
In this article, we study the relationship between notions of depth for sequences, namely, Bennett's notions of strong and weak depth, and deep $\Pi^0_1$ classes, introduced by the authors and motivated by previous work of Levin. For the first main result of the study, we show that every member of a $\Pi^0_1$ class is order-deep, a property that implies strong depth. From this result, we obtain new
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Logic Programming with Multiplicative Structures arXiv.cs.LO Pub Date : 2024-03-05 Matteo Acclavio, Roberto Maieli
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly represented using sequent calculi, in which each method is linked to an inference rule. In this context, proof search mirrors the program's execution. Previous works introduced
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Fuzzy Datalog$^\exists$ over Arbitrary t-Norms arXiv.cs.LO Pub Date : 2024-03-05 Matthias Lanzinger, Stefano Sferrazza, Przemysław A. Wałęga, Georg Gottlob
One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model predictions, structured databases, crowd-sourced data, and many more. To allow for such reasoning, we generalise the standard rule-based language Datalog with existential
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Unknown Biases and Timing Constraints in Timed Automata arXiv.cs.LO Pub Date : 2024-03-04 Darion Haase, Joost-Pieter Katoen
Timed automata are the formal model for real-time systems. Extensions with discrete probabilistic branching have been considered in the literature and successfully applied. Probabilistic timed automata (PTA) do require all branching probabilities and clock constraints to be constants. This report investigates PTA in which this constraint is relaxed: both branching probabilities and clock constraints
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Deciding Separation Logic with Pointer Arithmetic and Inductive Definitions arXiv.cs.LO Pub Date : 2024-03-04 Wanyun SuLCS, Zhilin WuLCS, Mihaela SighireanuLMF
Pointer arithmetic is widely used in low-level programs, e.g. memory allocators. The specification of such programs usually requires using pointer arithmetic inside inductive definitions to define the common data structures, e.g. heap lists in memory allocators. In this work, we investigate decision problems for SLAH, a separation logic fragment that allows pointer arithmetic inside inductive definitions
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Semi-Automated Modular Formal Verification of Critical Software: Liveness and Completeness Thresholds arXiv.cs.LO Pub Date : 2024-03-01 Tobias Reinhard
In this dissertation we describe two contributions to the state of the art in reasoning about liveness and safety, respectively. Programs for multiprocessor machines commonly perform busy waiting for synchronization. We propose the first separation logic for modularly verifying termination of such programs under fair scheduling. Our logic requires the proof author to associate a ghost signal with each
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DECIDER: A Rule-Controllable Decoding Strategy for Language Generation by Imitating Dual-System Cognitive Theory arXiv.cs.LO Pub Date : 2024-03-04 Chen Xu, Tian Lan, Changlong Yu, Wei Wang, Jun Gao, Yu Ji, Qunxi Dong, Kun Qian, Piji Li, Wei Bi, Bin Hu
Lexicon-based constrained decoding approaches aim to control the meaning or style of the generated text through certain target concepts. Existing approaches over-focus the targets themselves, leading to a lack of high-level reasoning about how to achieve them. However, human usually tackles tasks by following certain rules that not only focuses on the targets but also on semantically relevant concepts
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A Sufficient Epistemic Condition for Solving Stabilizing Agreement arXiv.cs.LO Pub Date : 2024-03-01 Giorgio Cignarale, Stephan Felber, Hugo Rincon Galeana
In this paper we provide a first-ever epistemic formulation of stabilizing agreement, defined as the non-terminating variant of the well established consensus problem. In stabilizing agreements, agents are given (possibly different) initial values, with the goal to eventually always decide on the same value. While agents are allowed to change their decisions finitely often, they are required to agree
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Representing Guardedness in Call-by-Value and Guarded Parametrized Monads arXiv.cs.LO Pub Date : 2024-03-01 Sergey Goncharov
Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles in various settings. In its most general form, the guardedness discipline applies to general symmetric monoidal categories and further specializes to Cartesian and
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Analyzing Divergence for Nondeterministic Probabilistic Models arXiv.cs.LO Pub Date : 2024-03-01 Hao Wu, Yuxi Fu, Huan Long, Xian Xu, Wenbo Zhang
Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several divergence-sensitive refinements of branching and weak probabilistic bisimilarities have been proposed in the literature. Both the definitions of these equivalences and
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Constructive S4 modal logics with the finite birelational frame property arXiv.cs.LO Pub Date : 2024-03-01 Philippe Balbiani, Martín Diéguez, David Fernández-Duque, Brett McLean
The logics $\mathsf{CS4}$ and $\mathsf{IS4}$ are the two leading intuitionistic variants of the modal logic $\mathsf{S4}$. Whether the finite model property holds for each of these logics have been long-standing open problems. It was recently shown that $\mathsf{IS4}$ has the finite frame property and thus the finite model property. In this paper, we prove that $\mathsf{CS4}$ also enjoys the finite
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Towards the verification of a generic interlocking logic: Dafny meets parameterized model checking arXiv.cs.LO Pub Date : 2024-02-29 Alessandro Cimatti, Alberto Griggio, Gianluca Redondi
Interlocking logics are at the core of critical systems controlling the traffic within stations. In this paper, we consider a generic interlocking logic, which can be instantiated to control a wide class of stations. We tackle the problem of parameterized verification, i.e. prove that the logic satisfies the required properties for all the relevant stations. We present a simplified case study, where
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Graph Homomorphism, Monotone Classes and Bounded Pathwidth arXiv.cs.LO Pub Date : 2024-03-01 Tala Eagling-Vose, Barnaby Martin, Daniel Paulusma, Mark Siggers, Siani Smith
A recent paper describes a framework for studying the computational complexity of graph problems on monotone classes, that is those omitting a set of graphs as a subgraph. If the problems lie in the framework, and many do, then the computational complexity can be described for all monotone classes defined by a finite set of omitted subgraphs. It is known that certain homomorphism problems, e.g. $C_5$-Colouring
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On the Counting Complexity of the Skolem Problem arXiv.cs.LO Pub Date : 2024-02-29 Gorav Jindal, Joël Ouaknine
The Skolem Problem asks, given an integer linear recurrence sequence (LRS), to determine whether the sequence contains a zero term or not. Its decidability is a longstanding open problem in theoretical computer science and automata theory. Currently, decidability is only known for LRS of order at most 4. On the other hand, the sole known complexity result is NP-hardness, due to Blondel and Portier
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Rewriting and Inductive Reasoning arXiv.cs.LO Pub Date : 2024-02-29 Márton Hajdu, Laura Kovács, Michael Rawson
Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive reasoning we show that we are missing crucial consequences. We therefore extend the superposition calculus with rewriting-based techniques to generate sufficient consequences
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Invariant Checking for SMT-based Systems with Quantifiers arXiv.cs.LO Pub Date : 2024-02-29 Gianluca Redondi, Alessandro Cimatti, Alberto Griggio, Kenneth McMillan
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort (finite, but unbounded) to an interpreted sort, such as the the integers under the theory of linear arithmetic. This formalism is very expressive and can be used for modeling
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Program Synthesis in Saturation arXiv.cs.LO Pub Date : 2024-02-29 Petra Hozzová, Laura Kovács, Chase Norman, Andrei Voronkov
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to both establish validity of this formula and discover program fragments satisfying the specification. As a result, when deriving a proof of program correctness, we
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Getting Saturated with Induction arXiv.cs.LO Pub Date : 2024-02-29 Márton Hajdu, Petra Hozzová, Laura Kovács, Giles Reger, Andrei Voronkov
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present
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Commonsense Ontology Micropatterns arXiv.cs.LO Pub Date : 2024-02-28 Andrew Eells, Brandon Dave, Pascal Hitzler, Cogan Shimizu
The previously introduced Modular Ontology Modeling methodology (MOMo) attempts to mimic the human analogical process by using modular patterns to assemble more complex concepts. To support this, MOMo organizes organizes ontology design patterns into design libraries, which are programmatically queryable, to support accelerated ontology development, for both human and automated processes. However,
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PiShield: A NeSy Framework for Learning with Requirements arXiv.cs.LO Pub Date : 2024-02-28 Mihaela Cătălina Stoian, Alex Tatomir, Thomas Lukasiewicz, Eleonora Giunchiglia
Deep learning models have shown their strengths in various application domains, however, they often struggle to meet safety requirements for their outputs. In this paper, we introduce PiShield, the first framework ever allowing for the integration of the requirements into the neural networks' topology. PiShield guarantees compliance with these requirements, regardless of input. Additionally, it allows
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Similarity-based analogical proportions arXiv.cs.LO Pub Date : 2024-02-28 Christian Antić
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical proportions by formulating the latter in terms of the former. The benefit of this similarity-based approach is that the connection between proportions and similarity is
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MCSat-based Finite Field Reasoning in the Yices2 SMT Solver arXiv.cs.LO Pub Date : 2024-02-27 Thomas Hader, Daniela Kaufmann, Ahmed Irfan, Stéphane Graham-Lengrand, Laura Kovács
This system description introduces an enhancement to the Yices2 SMT solver, enabling it to reason over non-linear polynomial systems over finite fields. Our reasoning approach fits into the model-constructing satisfiability (MCSat) framework and is based on zero decomposition techniques, which find finite basis explanations for theory conflicts over finite fields. As the MCSat solver within Yices2
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Superposition with Delayed Unification arXiv.cs.LO Pub Date : 2024-02-29 Ahmed Bhayat, Johannes Schoisswohl, Michael Rawson
Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that rely on unification procedures returning large or even infinite sets of unifiers, integrating unification into the calculus is an attractive method of dovetailing
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Equivariant ideals of polynomials arXiv.cs.LO Pub Date : 2024-02-27 Arka Ghosh, Sławomir Lasota
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming variables. First, we give a sufficient and necessary condition for A to guarantee the following generalisation of Hilbert's Basis Theorem: every polynomial ideal which
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Tree-Verifiable Graph Grammars arXiv.cs.LO Pub Date : 2024-02-26 Mark Chimes, Radu Iosif, Florian Zuleger
Hyperedge-Replacement grammars (HR) have been introduced by Courcelle in order to extend the notion of context-free sets from words and trees to graphs of bounded tree-width. While for words and trees the syntactic restrictions that guarantee that the associated languages of words resp. trees are regular - and hence, MSO-definable - are known, the situation is far more complicated for graphs. Here
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Quasi Directed Jonsson Operations Imply Bounded Width (For fo-expansions of symmetric binary cores with free amalgamation) arXiv.cs.LO Pub Date : 2024-02-26 Michal Wrona
Every CSP(B) for a finite structure B is either in P or it is NP-complete but the proofs of the finite-domain CSP dichotomy by Andrei Bulatov and Dimitryi Zhuk not only show the computational complexity separation but also confirm the algebraic tractability conjecture stating that tractability origins from a certain system of operations preserving B. The establishment of the dichotomy was in fact preceded
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How to avoid the commuting conversions of IPC arXiv.cs.LO Pub Date : 2024-02-25 José Espírito Santo, Gilda Ferreira
Since the observation in 2006 that it is possible to embed IPC into the atomic polymorphic lambda-calculus (a predicative fragment of system F with universal instantiations restricted to atomic formulas) different such embeddings appeared in the literature. All of them comprise the Russell-Prawitz translation of formulas, but have different strategies for the translation of proofs. Although these embeddings
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Effective MSO-Definability for Tree-width Bounded Models of an Inductive Separation Logic of Relations arXiv.cs.LO Pub Date : 2024-02-25 Lucas Bueri, Radu Iosif, Florian Zuleger
A class of graph languages is definable in Monadic Second-Order logic (MSO) if and only if it consists of sets of models of MSO formul{\ae}. If, moreover, there is a computable bound on the tree-widths of the graphs in each such set, the satisfiability and entailment problems are decidable, by Courcelle's Theorem. This motivates the comparison of other graph logics to MSO. In this paper, we consider
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Regular resolution effectively simulates resolution arXiv.cs.LO Pub Date : 2024-02-24 Sam Buss, Emre Yolcu
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs in regular resolution while admitting polynomial-size proofs in resolution. Thus, with respect to the usual notion of simulation, regular resolution is separated
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The Flower Calculus arXiv.cs.LO Pub Date : 2024-02-23 Pablo DonatoPARTOUT
We introduce the flower calculus, a deep inference proof system for intuitionistic first-order logic inspired by Peirce's existential graphs. It works as a rewriting system over inductive objects called "flowers", that enjoy both a graphical interpretation as topological diagrams, and a textual presentation as nested sequents akin to coherent formulas. Importantly, the calculus dispenses completely
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Interpretation of Inaccessible Sets in Martin-Löf Type Theory with One Mahlo Universe arXiv.cs.LO Pub Date : 2024-02-23 Yuta Takahashi
Martin-L\"{o}f type theory $\mathbf{MLTT}$ was extended by Setzer with the so-called Mahlo universe types. This extension is called $\mathbf{MLM}$ and was introduced to develop a variant of $\mathbf{MLTT}$ equipped with an analogue of a large cardinal. Another instance of constructive systems extended with an analogue of a large set was formulated in the context of Aczel's constructive set theory:
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Attractors of Parikh mapping iterations arXiv.cs.LO Pub Date : 2024-02-22 Alexander Chunikhin
Three types of the Parikh mapping are introduced, namely, alphabetic, alphabetic-basis and basis. Explicit expressions for attractors of the k-th order in bases n >= 8, including countable ones, are found. Properties for the alphabetic, alphabetic-basis and basis Parikh vectors are given at each step of the Parikh mapping. The maximum number of iterations leading to attractors of the k-th order in
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Representing Pedagogic Content Knowledge Through Rough Sets arXiv.cs.LO Pub Date : 2024-02-26 A Mani
A teacher's knowledge base consists of knowledge of mathematics content, knowledge of student epistemology, and pedagogical knowledge. It has severe implications on the understanding of student's knowledge of content, and the learning context in general. The necessity to formalize the different content knowledge in approximate senses is recognized in the education research literature. A related problem
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Machine-Checked Categorical Diagrammatic Reasoning arXiv.cs.LO Pub Date : 2024-02-22 Benoît Guillemet, Assia Mahboubi, Matthieu Piquerez
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language, which features dedicated proof commands to automate the synthesis, and the verification, of the technical parts often eluded in the literature.
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Model Checking Logical Actions in Magic Tricks arXiv.cs.LO Pub Date : 2024-02-21 Weijun Zhu
Some Magic Tricks (MT), such as many kinds of Card Magic (CM), consisting of human computational or logical actions. How to ensure the logical correctness of these MTs? In this paper, the Model Checking (MC) technique is employed to study a typical CM via a case study. First, computational operations of a CM called shousuigongcishi can be described by a Magic Algorithm (MAR). Second, the logical correctness
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Confluence of Logically Constrained Rewrite Systems Revisited arXiv.cs.LO Pub Date : 2024-02-21 Jonas Schöpf, Fabian Mitterwallner, Aart Middeldorp
We show that (local) confluence of terminating locally constrained rewrite systems is undecidable, even when the underlying theory is decidable. Several confluence criteria for logically constrained rewrite systems are known. These were obtained by replaying existing proofs for plain term rewrite systems in a constrained setting, involving a non-trivial effort. We present a simple transformation from
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Continuous Pushdown VASS in One Dimension are Easy arXiv.cs.LO Pub Date : 2024-02-20 Guillermo A. Perez, Shrisha Rao
A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static analysis of recursive programs manipulating integer variables. Unfortunately, reachability analysis, even for one-dimensional PVASS is not known to be decidable. We relax the model of one-dimensional PVASS to make
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homotopy.io: a proof assistant for finitely-presented globular $n$-categories arXiv.cs.LO Pub Date : 2024-02-20 Nathan Corbyn, Lukas Heidemann, Nick Hu, Chiara Sarti, Calin Tataru, Jamie Vicary
We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical representation. We describe the user interface and explain how the tool can be used in practice. We also describe the essential subsystems of the tool, including collapse
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Profinite trees, through monads and the lambda-calculus arXiv.cs.LO Pub Date : 2024-02-20 Vincent Moreau
In its simplest form, the theory of regular languages is the study of sets of finite words recognized by finite monoids. The finiteness condition on monoids gives rise to a topological space whose points, called profinite words, encode the limiting behavior of words with respect to finite monoids. Yet, some aspects of the theory of regular languages are not particular to monoids and can be described
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Modular Assurance of Complex Systems Using Contract-Based Design Principles arXiv.cs.LO Pub Date : 2024-02-20 Dag McGeorgeGroup Research and Development, DNV, Høvik, Norway, Jon Arne GlomsrudGroup Research and Development, DNV, Høvik, Norway
A growing number of safety-critical industries agree that building confidence in complex systems can be achieved through evidence and structured argumentation framed in assurance cases. Nevertheless, assurance cases can easily become too rigorous and difficult to develop and maintain when applied to complex systems. Therefore, we propose to use contract-based development (CBD), a method to manage complexity
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Assume-guarantee contract algebras are bounded Sugihara monoids arXiv.cs.LO Pub Date : 2024-02-19 Jose Luis Castiglioni, Rodolfo Ertola-Biraben
In [Incer Romeo, I. X., \textit{The Algebra of Contracts}. Ph.D. Thesis, UC Berkeley (2022)] an algebraic perspective on assume-guarantee contracts is proposed. This proposal relies heavily on a construction involving Boolean algebras. However, the structures thus proposed lack a clearly prescribed set of basic operations, necessary if we want to see them as a class of algebras (in the sense of Universal
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Conditional Logical Message Passing Transformer for Complex Query Answering arXiv.cs.LO Pub Date : 2024-02-20 Chongzhi Zhang, Zhiping Peng, Junhao Zheng, Qianli Ma
Complex Query Answering (CQA) over Knowledge Graphs (KGs) is a challenging task. Given that KGs are usually incomplete, neural models are proposed to solve CQA by performing multi-hop logical reasoning. However, most of them cannot perform well on both one-hop and multi-hop queries simultaneously. Recent work proposes a logical message passing mechanism based on the pre-trained neural link predictors
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Automating Boundary Filling in Cubical Agda arXiv.cs.LO Pub Date : 2024-02-19 Maximilian Doré, Evan Cavallo, Anders Mörtberg
When working in a proof assistant, automation is key to discharging routine proof goals such as equations between algebraic expressions. Homotopy Type Theory allows the user to reason about higher structures, such as topological spaces, using higher inductive types (HITs) and univalence. Cubical Agda is an extension of Agda with computational support for HITs and univalence. A difficulty when working
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Mirroring Call-by-Need, or Values Acting Silly arXiv.cs.LO Pub Date : 2024-02-19 Beniamino Accattoli, Adrienne Lancelot
Call-by-need evaluation for the lambda-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how duplication and erasure can be combined, we design a degenerated calculus, dubbed call-by-silly, that is symmetric to call-by-need in that it merges the worst of call-by-name
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Type Isomorphisms for Multiplicative-Additive Linear Logic arXiv.cs.LO Pub Date : 2024-02-19 Rémi Di GuardiaLIP, PLUME, Olivier LaurentLIP, PLUME
We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo. This yields a much richer equational theory involving distributivity and cancellation laws. The unit-free case is obtained by relying on the proof-net syntax introduced by
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Towards benchmarking of Solidity verification tools arXiv.cs.LO Pub Date : 2024-02-16 Massimo Bartoletti, Fabio Fioravanti, Giulia Matricardi, Roberto Pettinau, Franco Sainas
Formal verification of smart contracts has become a hot topic in academic and industrial research, given the growing value of assets managed by decentralized applications and the consequent incentive for adversaries to tamper with them. Most of the current research on the verification of contracts revolves around Solidity, the main high-level language supported by Ethereum and other leading blockchains
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Spanning Matrices via Satisfiability Solving arXiv.cs.LO Pub Date : 2024-02-16 Clemens Eisenhofer, Michael Rawson, Laura Kovács
We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number of drawbacks in the context of satisfiability solving. The matrix setting permits numerous global refinements of the basic connection calculus. We also show that
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Mechanised uniform interpolation for modal logics K, GL and iSL arXiv.cs.LO Pub Date : 2024-02-16 Hugo Férée, Iris van der Giessen, Sam van Gool, Ian Shillito
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) G\"odel-L\"ob logic GL, for which our formalisation clarifies an important point in
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Parallel Play Saves Quantifiers arXiv.cs.LO Pub Date : 2024-02-15 Marco Carmosino, Ronald Fagin, Neil Immerman, Phokion Kolaitis, Jonathan Lenchner, Rik Sengupta, Ryan Williams
The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call "parallel play", that dramatically reduces the number of quantifiers needed in many cases. Linear orders and strings are the most basic representatives of ordered structures
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Cloud Kitchen: Using Planning-based Composite AI to Optimize Food Delivery Process arXiv.cs.LO Pub Date : 2024-02-16 Slavomír Švancár, Lukáš Chrpa, Filip Dvořák, Tomáš Balyo
The global food delivery market provides many opportunities for AI-based services that can improve the efficiency of feeding the world. This paper presents the Cloud Kitchen platform as a decision-making tool for restaurants with food delivery and a simulator to evaluate the impact of the decisions. The platform consists of a Technology-Specific Bridge (TSB) that provides an interface for communicating
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Overapproximation of Non-Linear Integer Arithmetic for Smart Contract Verification arXiv.cs.LO Pub Date : 2024-02-15 Petra Hozzová, Jaroslav Bendík, Alexander Nutz, Yoav Rodeh
The need to solve non-linear arithmetic constraints presents a major obstacle to the automatic verification of smart contracts. In this case study we focus on the two overapproximation techniques used by the industry verification tool Certora Prover: overapproximation of non-linear integer arithmetic using linear integer arithmetic and using non-linear real arithmetic. We compare the performance of