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A minimal base or a direct base? That is the question! arXiv.cs.LO Pub Date : 2024-04-18 Jaume Baixeries, Amedeo Napoli
In this paper we revisit the problem of computing the closure of a set of attributes, given a set of Armstrong dependencies. This problem is of main interest in logics, in the relational database model, in lattice theory and in Formal Concept Analysis as well. We consider here three main closure algorithms, namely Closure, LinClosure and Wild's Closure, which are combined with implication bases which
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Symbolic Computation for All the Fun arXiv.cs.LO Pub Date : 2024-04-18 Chad E. Brown, Mikoláš Janota, Mirek Olšák
Motivated by the recent 10 million dollar AIMO challenge, this paper targets the problem of finding all functions conforming to a given specification. This is a popular problem at mathematical competitions and it brings about a number of challenges, primarily, synthesizing the possible solutions and proving that no other solutions exist. Often, there are infinitely many solutions and then the set of
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On the Unprovability of Circuit Size Bounds in Intuitionistic $\mathsf{S}^1_2$ arXiv.cs.LO Pub Date : 2024-04-18 Lijie Chen, Jiatu Li, Igor C. Oliveira
We show that there is a constant $k$ such that Buss's intuitionistic theory $\mathsf{IS}^1_2$ does not prove that SAT requires co-nondeterministic circuits of size at least $n^k$. To our knowledge, this is the first unconditional unprovability result in bounded arithmetic in the context of worst-case fixed-polynomial size circuit lower bounds. We complement this result by showing that the upper bound
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Multi-modalities and non-commutativity/associativity in functorial linear logic: a case study arXiv.cs.LO Pub Date : 2024-04-17 Carlos Olarte, Elaine Pimentel
Similar to modal connectives, the exponential ! in intuitionistic linear logic (ILL) is not canonical, in the sense that if $i\not= j$ then $!^i F\not\equiv !^j F$. Intuitively, this means that we can mark the exponential with labels taken from a set I organized in a pre-order $\preceq$, obtaining (possibly infinitely-many) exponentials ($!^i$ for $i\in I$). There are, however, two main differences
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The General and Finite Satisfiability Problems for PCTL are Undecidable arXiv.cs.LO Pub Date : 2024-04-16 Miroslav Chodil, Antonín Kučera
The general/finite PCTL satisfiability problem asks whether a given PCTL formula has a general/finite model. We show that the finite PCTL satisfiability problem is undecidable, and the general PCTL satisfiability problem is even highly undecidable (beyond the arithmetical hierarchy). Consequently, there are no sound deductive systems proving all generally/finitely valid PCTL formulae.
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On Homomorphism Indistinguishability and Hypertree Depth arXiv.cs.LO Pub Date : 2024-04-16 Benjamin Scheidt
$GC^k$ is a logic introduced by Scheidt and Schweikardt (2023) to express properties of hypergraphs. It is similar to first-order logic with counting quantifiers ($C$) adapted to the hypergraph setting. It has distinct sets of variables for vertices and for hyperedges and requires vertex variables to be guarded by hyperedge variables on every quantification. We prove that two hypergraphs $G$, $H$ satisfy
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One is all you need: Second-order Unification without First-order Variables arXiv.cs.LO Pub Date : 2024-04-16 David M. Cerna, Julian Parsert
We consider the fragment of Second-Order unification with the following properties: (i) only one second-order variable allowed, (ii) first-order variables do not occur. We show that Hilbert's 10$^{th}$ problem is reducible to this fragment if the signature contains a binary function symbol and two constants. This generalizes known undecidability results. Furthermore, We show that adding the following
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Complete Game Logic with Sabotage arXiv.cs.LO Pub Date : 2024-04-15 Noah Abou El Wafa, André Platzer
We introduce Sabotage Game Logic ($\mathsf{GL_s}$), a simple and natural extension of Parikh's Game Logic with a single additional primitive, which allows players to lay traps for the opponent to avoid. $\mathsf{GL_s}$ can be used to model infinite sabotage games, in which players can change the rules during game play. In contrast to Game Logic, which is strictly less expressive, GLs is exactly as
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Computable domains of a Halting Function arXiv.cs.LO Pub Date : 2024-04-15 Abel Luis Peralta
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing in 1936 in his foundational work "On Computable Numbers". Here we face it using the Model of computability of the recursive functions instead of the Turing's machines
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A Uniform Framework for Language Inclusion Problems arXiv.cs.LO Pub Date : 2024-04-15 Kyveli Doveri, Pierre Ganty, Chana Weil-Kennedy
We present a uniform approach for solving language inclusion problems. Our approach relies on a least fixpoint characterization and a quasiorder to compare words of the "smaller" language, reducing the inclusion check to a finite number of membership queries in the "larger" language. We present our approach in detail on the case of inclusion of a context-free language given by a grammar into a regular
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Learn from Failure: Fine-Tuning LLMs with Trial-and-Error Data for Intuitionistic Propositional Logic Proving arXiv.cs.LO Pub Date : 2024-04-10 Chenyang An, Zhibo Chen, Qihao Ye, Emily First, Letian Peng, Jiayun Zhang, Zihan Wang, Sorin Lerner, Jingbo Shang
Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful proof paths, faces a discrepancy at the inference stage, as it must sample and try various tactics at each proof state until finding success, unlike its training
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A Semantic Proof of Generalised Cut Elimination for Deep Inference arXiv.cs.LO Pub Date : 2024-04-09 Robert Atkey, Wen Kokke
Multiplicative-Additive System Virtual (MAV) is a logic that extends Multiplicative-Additive Linear Logic with a self-dual non-commutative operator expressing the concept of "before" or "sequencing". MAV is also an extenson of the the logic Basic System Virtual (BV) with additives. Formulas in BV have an appealing reading as processes with parallel and sequential composition. MAV adds internal and
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Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version arXiv.cs.LO Pub Date : 2024-04-09 Nick Bezhanishvili, Vincenzo Ciancia, David Gabelaia, Mamuka Jibladze, Diego Latella, Mieke Massink, Erik P. de Vink
In the context of spatial logics and spatial model checking for polyhedral models - mathematical basis for visualisations in continuous space - we propose a weakening of simplicial bisimilarity. We additionally propose a corresponding weak notion of +/--bisimilarity on cell-poset models, a discrete representation of polyhedral models. We show that two points are weakly simplicial bisimilar iff their
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Syndicate: Synergistic Synthesis of Ranking Function and Invariants for Termination Analysis arXiv.cs.LO Pub Date : 2024-04-09 Yasmin Sarita, Avaljot Singh, Shaurya Gomber, Gagandeep Singh, Mahesh Vishwanathan
Several techniques have been developed to prove the termination of programs. Finding ranking functions is one of the common approaches to do so. A ranking function must be bounded and must reduce at every iteration for all the reachable program states. Since the set of reachable states is often unknown, invariants serve as an over-approximation. Further, in the case of nested loops, the initial set
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Teaching Higher-Order Logic Using Isabelle arXiv.cs.LO Pub Date : 2024-04-08 Simon Tobias LundTechnical University of Denmark, Jørgen VilladsenTechnical University of Denmark
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good introduction for someone looking into learning about higher-order logic and proof assistants, without having to study the much more complex Isabelle/HOL with heavier
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On the complexity of normalization for the planar $λ$-calculus arXiv.cs.LO Pub Date : 2024-04-08 Anupam Das, Damiano Mazza, Lê Thành Dũng Nguyên, Noam Zeilberger
We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.
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Function spaces for orbit-finite sets arXiv.cs.LO Pub Date : 2024-04-08 Mikołaj Bojańczyk, Lê Thành Dũng Nguyên, Rafał Stefański
Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are orbit-finite sets, then the space of finitely supported functions from X to Y is not orbit-finite. In this paper we propose two solutions to this problem: one is obtained
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The Church Synthesis Problem over Continuous Time arXiv.cs.LO Pub Date : 2024-04-07 Alexander Rabinovich, Daniel Fattal
The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators
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Iof-maint -- Modular maintenance ontology arXiv.cs.LO Pub Date : 2024-04-08 Melinda Hodkiewicz, Caitlin Woods, Matt Selway, Markus Stumptner
In this paper we present a publicly-available maintenance ontology (Iof-maint). Iof-maint is a modular ontology aligned with the Industrial Ontology Foundry Core (IOF Core) and contains 20 classes and 2 relations. It provides a set of maintenance-specific terms used in a wide variety of practical data-driven use cases. Iof-maint supports OWL DL reasoning, is documented, and is actively maintained on
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Refutability as Recursive as Provability arXiv.cs.LO Pub Date : 2024-04-05 Paola Cattabriga
Godel numbering is an arithmetization of sintax which defines provability by coding a primitive recursive predicate, Pf(x,v). A multiplicity of researches and results all around this well-known recursive predicate are today widespread in many areas of logic and AI. Not equally investigated is the refutability predicate defined by Godel numbering within the same primitive recursive status. Rf(x,v) can
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Implicit automata in λ-calculi III: affine planar string-to-string functions arXiv.cs.LO Pub Date : 2024-04-05 Cécilia Pradic, Ian Price
We prove a characterization of first-order string-to-string transduction via $\lambda$-terms typed in non-commutative affine logic that compute with Church encoding, extending the analogous known characterization of star-free languages. We show that every first-order transduction can be computed by a $\lambda$-term using a known Krohn-Rhodes-style decomposition lemma. The converse direction is given
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Bringing memory to Boolean networks: a unifying framework arXiv.cs.LO Pub Date : 2024-04-04 Maximilien Gadouleau, Loïc Paulevé, Sara Riva
Boolean networks are extensively applied as models of complex dynamical systems, aiming at capturing essential features related to causality and synchronicity of the state changes of components along time. Dynamics of Boolean networks result from the application of their Boolean map according to a so-called update mode, specifying the possible transitions between network configurations. In this paper
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Permissible Knowledge Pooling arXiv.cs.LO Pub Date : 2024-04-04 Huimin Dong
Information pooling has been extensively formalised across various logical frameworks in distributed systems, characterized by diverse information-sharing patterns. These approaches generally adopt an intersection perspective, aggregating all possible information, regardless of whether it is known or unknown to the agents. In contrast, this work adopts a unique stance, emphasising that sharing knowledge
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Alternating Quantifiers in Uniform One-Dimensional Fragments with an Excursion into Three-Variable Logic arXiv.cs.LO Pub Date : 2024-04-04 Oskar Fiuk, Emanuel Kieronski
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in blocks, each block consisting only of existential quantifiers or only of universal quantifiers. In this paper we consider the possibility of mixing both types of quantifiers
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Non-wellfounded parsimonious proofs and non-uniform complexity arXiv.cs.LO Pub Date : 2024-04-04 Matteo Acclavio, Gianluca Curzi, Giulio Guerrieri
In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. We present non-wellfounded parsimonious proof systems capturing the classes $\mathbf{FPTIME}$ and $\mathbf{FP}/\mathsf{poly}$. Soundness is established
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Interpolant Existence is Undecidable for Two-Variable First-Order Logic with Two Equivalence Relations arXiv.cs.LO Pub Date : 2024-04-03 Frank Wolter, Michael Zakharyaschev
The interpolant existence problem (IEP) for a logic L is to decide, given formulas P and Q, whether there exists a formula I, built from the shared symbols of P and Q, such that P entails I and I entails Q in L. If L enjoys the Craig interpolation property (CIP), then the IEP reduces to validity in L. Recently, the IEP has been studied for logics without the CIP. The results obtained so far indicate
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Commutative N-polyregular functions arXiv.cs.LO Pub Date : 2024-04-02 Aliaume Lopez
This paper addresses two questions regarding N-polyregular functions, that forms a proper subset of N-rational series. We show that given a Z-rational series, it is decidable whether it is computable via a commutative N-polyregular function, and provide a counter-example to the theorem of Karhum\"aki that studied the same question in the case of polynomials. We also prove that it is decidable whether
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Techniques for Measuring the Inferential Strength of Forgetting Policies arXiv.cs.LO Pub Date : 2024-04-03 Patrick Doherty, Andrzej Szalas
The technique of forgetting in knowledge representation has been shown to be a powerful and useful knowledge engineering tool with widespread application. Yet, very little research has been done on how different policies of forgetting, or use of different forgetting operators, affects the inferential strength of the original theory. The goal of this paper is to define loss functions for measuring changes
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Classifying Graphemes in English Words Through the Application of a Fuzzy Inference System arXiv.cs.LO Pub Date : 2024-04-02 Samuel Rose, Chandrasekhar Kambhampati
In Linguistics, a grapheme is a written unit of a writing system corresponding to a phonological sound. In Natural Language Processing tasks, written language is analysed through two different mediums, word analysis, and character analysis. This paper focuses on a third approach, the analysis of graphemes. Graphemes have advantages over word and character analysis by being self-contained representations
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Towards a semantic characterisation of global type well-formedness arXiv.cs.LO Pub Date : 2024-03-30 Ilaria Castellani, Paola Giannini
We address the question of characterising the well-formedness properties of multiparty session types semantically, i.e., as properties of the semantic model used to interpret types. Choosing Prime Event Structures (PESs) as our semantic model, we present semantic counterparts for the two properties that underpin global type well-formedness, namely projectability and boundedness, in this model. As a
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Regular Games with Imperfect Information Are Not That Regular arXiv.cs.LO Pub Date : 2024-03-29 Laurent Doyen, Thomas Soullard
We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other player. Imperfect information is modeled by an indistinguishability relation %that describing the pairs of histories that the first player cannot distinguish, a generalization
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Linear Programming in Isabelle/HOL arXiv.cs.LO Pub Date : 2024-03-28 Julian Parsert
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This allows formally proving its soundness, termination, and other properties. We base these results on a previous formalisation of the simplex algorithm which does not take
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EDA-Driven Preprocessing for SAT Solving arXiv.cs.LO Pub Date : 2024-03-28 Zhengyuan Shi, Tiebing Tang, Sadaf Khan, Hui-Ling Zhen, Mingxuan Yuan, Zhufei Chu, Qiang Xu
Effective formulation of problems into Conjunctive Normal Form (CNF) is critical in modern Boolean Satisfiability (SAT) solving for optimizing solver performance. Addressing the limitations of existing methods, our Electronic Design Automation (EDA)-driven preprocessing framework introduces a novel methodology for preparing SAT instances, leveraging both circuit and CNF formats for enhanced flexibility
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Deciding Boolean Separation Logic via Small Models (Technical Report) arXiv.cs.LO Pub Date : 2024-03-27 Tomáš Dacík, Adam Rogalewicz, Tomáš Vojnar, Florian Zuleger
We present a novel decision procedure for a fragment of separation logic (SL) with arbitrary nesting of separating conjunctions with boolean conjunctions, disjunctions, and guarded negations together with a support for the most common variants of linked lists. Our method is based on a model-based translation to SMT for which we introduce several optimisations$\unicode{x2013}$the most important of them
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Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic arXiv.cs.LO Pub Date : 2024-03-27 Peter Habermehl, Michal Hečko, Vojtěch Havlena, Lukáš Holík, Ondřej Lengál
We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work directly with numbers. This combination is enabled by a fine-grained version of the duality between automata and arithmetic formulae. In particular, we employ a construction
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Logic and Languages of Higher-Dimensional Automata arXiv.cs.LO Pub Date : 2024-03-28 Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, Marie Fortin
In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (iiPoms<=k) closed under order extension. We prove that languages of HDAs are MSO-definable. For the converse, we show that the order extensions of MSO-definable sets of iiPoms<=k are languages of HDAs. As a consequence
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Formally Modelling the Rijkswaterstaat Tunnel Control Systems in a Constrained Industrial Environment arXiv.cs.LO Pub Date : 2024-03-27 Kevin H. J. JilissenRijkswaterstaat, Peter DielemanRijkswaterstaat, Jan Friso GrooteEindhoven University of Technology
Rijkswaterstaat, the National Dutch body responsible for infrastructure, recognised the importance of formal modelling and set up a program to model the control of road tunnels. This is done to improve the standardisation of tunnel control and make communication with suppliers smoother. A subset of SysML is used to formulate the models, which are substantial. In an earlier paper we have shown that
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Synergistic Knowledge arXiv.cs.LO Pub Date : 2024-03-27 Christian Cachin, David Lehnherr, Thomas Studer
In formal epistemology, group knowledge is often modelled as the knowledge that the group would have, if the agents shared all their individual knowledge. However, this interpretation does not account for relations between agents. In this work, we propose the notion of synergistic knowledge which makes it possible to model those relationships.
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On Propositional Dynamic Logic and Concurrency arXiv.cs.LO Pub Date : 2024-03-27 Matteo Acclavio, Fabrizio Montesi, Marco Peressotti
Dynamic logic in the setting of concurrency has proved problematic because of the challenge of capturing interleaving. This challenge stems from the fact that the operational semantics for programs considered in these logics is tailored on trace reasoning for sequential programs. In this work, we generalise propositional dynamic logic (PDL) to a logic framework we call operational propositional dynamic
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A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq arXiv.cs.LO Pub Date : 2024-03-27 Reynald Affeldt, Zachary Stone
Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation Theorem formalized in the Coq proof assistant, from which the first Fundamental Theorem of Calculus (FTC) for the Lebesgue integral is obtained as a corollary. Proving
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Formal Verification of the Empty Hexagon Number arXiv.cs.LO Pub Date : 2024-03-26 Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, Marijn J. H. Heule
A recent breakthrough in computer-assisted mathematics showed that every set of $30$ points in the plane in general position (i.e., without three on a common line) contains an empty convex hexagon, thus closing a line of research dating back to the 1930s. Through a combination of geometric insights and automated reasoning techniques, Heule and Scheucher constructed a CNF formula $\phi_n$, with $O(n^4)$
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SAT Encoding of Partial Ordering Models for Graph Coloring Problems arXiv.cs.LO Pub Date : 2024-03-23 Daniel Faber, Adalat Jabrayilov, Petra Mutzel
In this paper, we suggest new SAT encodings of the partial-ordering based ILP model for the graph coloring problem (GCP) and the bandwidth coloring problem (BCP). The GCP asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. The BCP is a generalization, where each edge has a weight that enforces a minimal
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Formally Verifying the Safety of Pipelined Moonshot Consensus Protocol arXiv.cs.LO Pub Date : 2024-03-25 M. Praveen, Raghavendra Ramesh, Isaac Doidge
Decentralized Finance (DeFi) has emerged as a contemporary competitive as well as complementary to traditional centralized finance systems. As of 23rd January 2024, per Defillama approximately USD 55 billion is the total value locked on the DeFi applications on all blockchains put together. A Byzantine Fault Tolerant (BFT) State Machine Replication (SMR) protocol, popularly known as the consensus protocol
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(Towards a) Statistical Probabilistic Lazy Lambda Calculus arXiv.cs.LO Pub Date : 2024-03-22 Radha Jagadeesan
We study the desiderata on a model for statistical probabilistic programming languages. We argue that they can be met by a combination of traditional tools, namely open bisimulation and probabilistic simulation.
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Chase Termination Beyond Polynomial Time arXiv.cs.LO Pub Date : 2024-03-25 Philipp Hanisch, Markus Krötzsch
The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to terminate. Many decidable conditions have been proposed for tgds to ensure chase termination, typically by forbidding some kind of "cycle" in the chase process.
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PECR: A formal system based on computability logic arXiv.cs.LO Pub Date : 2024-03-21 G. Pantelis
PECR is a formal system designed to explore the properties of computability of programs on a real-world computer. As such PECR incorporates the finite resources of the machine upon which a program is to be executed. The main features of the formal system will be presented and its practical applications will be discussed. Of particular interest is the implementation of the formal system to the exploration
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Fully Evaluated Left-Sequential Logics arXiv.cs.LO Pub Date : 2024-03-21 Alban Ponse, Daan J. C. Staudt
We consider a family of two-valued "fully evaluated left-sequential logics" (FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing (weakest) and immune to atomic side effects. Next is Memorising FEL, in which evaluations of subexpressions are memorised. The following stronger logic is Conditional FEL (inspired by Guzm\'an and Squier's Conditional logic, 1990). The strongest FEL
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Complexity of the Model Checking problem for inquisitive propositional and modal logic arXiv.cs.LO Pub Date : 2024-03-21 Gianluca Grilletti, Ivano Ciardelli
The aim of this paper is to study the complexity of the model checking problem MC for inquisitive propositional logic InqB and for inquisitive modal logic InqM, that is, the problem of deciding whether a given finite structure for the logic satisfies a given formula. In recent years, this problem has been thoroughly investigated for several variations of dependence and teams logics, systems closely
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The equational theory of the Weihrauch lattice with multiplication arXiv.cs.LO Pub Date : 2024-03-20 Eike Neumann, Arno Pauly, Cécilia Pradic
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite parallelization $(-)^*$ which are true however we substitute Weihrauch degrees for the variables. We provide a combinatorial description of these in terms of a reducibility
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Database Dependencies and Formal Concept Analysis arXiv.cs.LO Pub Date : 2024-03-20 Jaume Baixeries
This is an account of the characterization of database dependencies with Formal Concept Analysis.
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Taming Differentiable Logics with Coq Formalisation arXiv.cs.LO Pub Date : 2024-03-20 Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia Ślusarz, Kathrin Stark
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to translate propositional or first-order formulae into loss functions deployed for optimisation in machine learning. At the same time, recent attempts to give programming
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Reasoning about distributive laws in a concurrent refinement algebra arXiv.cs.LO Pub Date : 2024-03-20 Larissa A. Meinicke, Ian J. Hayes
Distributive laws are important for algebraic reasoning in arithmetic and logic. They are equally important for algebraic reasoning about concurrent programs. In existing theories such as Concurrent Kleene Algebra, only partial correctness is handled, and many of its distributive laws are weak, in the sense that they are only refinements in one direction, rather than equalities. The focus of this paper
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Mechanized HOL Reasoning in Set Theory arXiv.cs.LO Pub Date : 2024-03-20 Simon Guilloud, Sankalp Gambhir, Andrea Gilot, Viktor Kunčak
We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on axiomatic set theory. HOL proof steps are implemented as proof producing tactics in Lisa, and the types are interpreted as sets, with function (or arrow) types coinciding
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Answer Set Programming for Flexible Payroll Management arXiv.cs.LO Pub Date : 2024-03-19 Benjamin Callewaert, Joost Vennekens
Payroll management is a critical business task that is subject to a large number of rules, which vary widely between companies, sectors, and countries. Moreover, the rules are often complex and change regularly. Therefore, payroll management systems must be flexible in design. In this paper, we suggest an approach based on a flexible Answer Set Programming (ASP) model and an easy-to-read tabular representation
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Regularization in Spider-Style Strategy Discovery and Schedule Construction arXiv.cs.LO Pub Date : 2024-03-19 Filip Bártek, Karel Chvalovský, Martin Suda
To achieve the best performance, automatic theorem provers often rely on schedules of diverse proving strategies to be tried out (either sequentially or in parallel) on a given problem. In this paper, we report on a large-scale experiment with discovering strategies for the Vampire prover, targeting the FOF fragment of the TPTP library and constructing a schedule for it, based on the ideas of Andrei
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Enhancing Formal Theorem Proving: A Comprehensive Dataset for Training AI Models on Coq Code arXiv.cs.LO Pub Date : 2024-03-19 Andreas Florath
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the specialized nature of Coq syntax and semantics poses unique challenges for Large Language Models (LLMs). Addressing this gap, we present a comprehensive dataset specifically
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The interpolant existence problem for weak K4 and difference logic arXiv.cs.LO Pub Date : 2024-03-17 Agi Kurucz, Frank Wolter, Michael Zakharyaschev
As well known, weak K4 and the difference logic DL do not enjoy the Craig inter- polation property. Our concern here is the problem of deciding whether any given implication does have an interpolant in these logics. We show that the nonexistence of an interpolant can always be witnessed by a pair of bisimilar models of polynomial size for DL and of triple-exponential size for weak K4, and so the interpolant
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EXPLORER: Exploration-guided Reasoning for Textual Reinforcement Learning arXiv.cs.LO Pub Date : 2024-03-15 Kinjal Basu, Keerthiram Murugesan, Subhajit Chaudhury, Murray Campbell, Kartik Talamadupula, Tim Klinger
Text-based games (TBGs) have emerged as an important collection of NLP tasks, requiring reinforcement learning (RL) agents to combine natural language understanding with reasoning. A key challenge for agents attempting to solve such tasks is to generalize across multiple games and demonstrate good performance on both seen and unseen objects. Purely deep-RL-based approaches may perform well on seen
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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