Tree Semantics Research Articles

The Images of Sacred Trees in Ancient Egyptian Fairy Tales

The paper examines the semantics of trees described in the ancient Egyptian fairy tales “Tale of Two Brothers” and in the “Story of Sinuhe”. The purpose of the study is to identify the semantics of trees in these fairy tales, their relationship with the religious ideas of the Egyptians and specifies of ideas about the calendar cycle displayed in these texts. The author traces literary parallels between the images of fairy-tale trees and the motifs of the “Book of the Dead”, which tells about the posthumous life of the soul of the deceased in the Netherworld. The study reveals that in the “Tale of Two Brothers”, the cedar and two persea trees are correlated with the Osiris and solar cults. The persea trees represent the rays of the sun, Osiris and the deceased as the blessed spirit Akh. The cedar inflorescence located at the top of the tree is also associated with the image of the sun. It was found that in this fairy tale, the description of tree life and the hero’s repeated birth reflect the change of calendar cycles from the flood season to the harvest season, from the period of visibility of celestial bodies and plants to the period of their invisibility. The sycamore, mentioned in the “Story of Sinuhe”, is the sacred tree of Hathor, Isis and Nut and appears as a symbol of the heaven with which these goddesses were associated.

СЕМАНТИКА И ФУНКЦИИ ДЕРЕВЬЕВ В РАМКАХ СЮЖЕТНОГО ТИПА 1877* «ЧЕЛОВЕК В ДУПЛЕ»

The article is devoted to the analysis of the semantics of trees in an anecdotal fairy tale. The research material was Russian and Belarusian fairy tales. The article uses the technique of frame analysis of the fairy tale motif and plot, proposed by S.Yu. Neklyudov. The fairy tale type 1877* is a frame consisting of six slots: wandering in the forest, moving to a tree, imprisonment in a hollow, lumberjacks, contact with lumberjacks, liberation. The semantics of the fairy tale is closely related to the mythology of trees. The hero’s stay in the tree is interpreted as a temporary death. This determines the objective world of the fairy tale, within which trees acquire such household allomorphs as a barrel, a chest, a beehive, a trough, and the hero is compared with a bee.

How to early integrate operational diagnosis objectives in model‐driven engineering processes: A methodological proposal based on fault and behavior trees

AbstractTo help operators perform their diagnosis tasks more efficiently, the authors put forward a novel methodology introducing a new type of model, dedicated to operations, co‐created in parallel with the design models, in the preliminary stages of system development, using the language semantics of behavior trees. In this paper, the authors present the need for this new model type as expressed by the industry and justify their choice for adopting behavior trees, while illustrating in detail the proposed methodology.

Explanatory Denotational Semantics for Complex Event Patterns

Recent years brought popularity and importance of complex event processing (CEP) and associated query languages. CEP systems can be hard to understand. It is often non-trivial to determine streams of events matched by a query, and sometimes we may not notice important edge cases. Hence, the desirability of formal semantics permitting reasoning about resulting complex events and checking if actual matchings agree with our intentions follows. In the article, we introduce a pattern language PatLang with some unique syntactic features related to variable binding. We provide two distinct denotational semantics for PatLang : Minimal semantics , sufficient to describe when patterns match, and tree semantics , which provides detailed information about subpatterns with which the matched events actually match, i.e., information about interpretation of matched events induced by the pattern matching. The tree semantics is unnecessary for verifying correctness of pattern matching execution. However, we show that neither minimal semantics, nor semantics from the prior work suffices to effectively locate errors in patterns with respect to their intended meaning, and that the additional information provided by the tree semantics is crucial for that purpose. We prove that tree semantics can be mapped to minimal semantics. Finally, we provide some practical evaluation.

Efficient and Generic Algorithms for Quantitative Attack Tree Analysis

Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantify how good the security of a system is; typical metrics being the most likely attack, the cheapest, or the most damaging one. However, existing methods are only geared towards specific metrics or do not work on general attack trees. This paper classifies attack trees in two dimensions: proper trees vs. directed acyclic graphs (i.e. with shared subtrees); and static vs. dynamic gates. For three out of these four classes, we propose novel algorithms that work over a generic attribute domain, encompassing a large number of concrete security metrics defined on the attack tree semantics; dynamic attack trees with directed acyclic graph structure are left as an open problem. We also analyse the computational complexity of our methods.

Sound static analysis of regular expressions for vulnerabilities to denial of service attacks

Modern programming languages often provide functions to manipulate regular expressions in standard libraries. If they offer support for advanced features, the matching algorithm has an exponential worst-case time complexity: for some so-called vulnerable regular expressions, an attacker can craft ad hoc strings to force the matcher to exhibit an exponential behavior and perform a Regular Expression Denial of Service (ReDoS) attack. In this paper, we introduce a framework based on a tree semantics to statically identify ReDoS vulnerabilities. In particular, we put forward an algorithm to extract an overapproximation of the set of words that are dangerous for a regular expression, effectively catching all possible attacks. We have implemented the analysis in a tool called rat, and testing it on a dataset of 74,669 regular expressions, we observed that in 99.78% of the instances the analysis terminates in less than one second. We compared rat to seven other ReDoS detectors, and we found that our tool is faster, often by orders of magnitude, than most other tools. While raising a low number of false positives, rat is the only ReDoS detector that does not report false negatives.

Adversarial Formal Semantics of Attack Trees and Related Problems

Security is a subject of increasing attention in our actual society in order to protect critical resources from information disclosure, theft or damage. The informal model of attack trees introduced by Schneier, and widespread in the industry, is advocated in the 2008 NATO report to govern the evaluation of the threat in risk analysis. Attack-defense trees have since been the subject of many theoretical works addressing different formal approaches. In 2017, M. Audinot et al. introduced a path semantics over a transition system for attack trees. Inspired by the later, we propose a two-player interpretation of the attack-tree formalism. To do so, we replace transition systems by concurrent game arenas and our associated semantics consist of strategies. We then show that the emptiness problem, known to be NP-complete for the path semantics, is now PSPACE-complete. Additionally, we show that the membership problem is coNP-complete for our two-player interpretation while it collapses to P in the path semantics.

Taylor subsumes Scott, Berry, Kahn and Plotkin

The speculative ambition of replacing the old theory of program approximation based on syntactic continuity with the theory of resource consumption based on Taylor expansion and originating from the differential λ-calculus is nowadays at hand. Using this resource sensitive theory, we provide simple proofs of important results in λ-calculus that are usually demonstrated by exploiting Scott’s continuity, Berry’s stability or Kahn and Plotkin’s sequentiality theory. A paradigmatic example is given by the Perpendicular Lines Lemma for the Böhm tree semantics, which is proved here simply by induction, but relying on the main properties of resource approximants: strong normalization, confluence and linearity.

Attribute evaluation on attack trees with incomplete information

Attack trees are considered a useful tool for security modelling because they support qualitative as well as quantitative analysis. The quantitative approach is based on values associated to each node in the tree, expressing, for instance, the minimal cost or probability of an attack. Current quantitative methods for attack trees allow the analyst to, based on an initial assignment of values to the leaf nodes, derive the values of the higher nodes in the tree. In practice, however, it shows to be very difficult to obtain reliable values for all leaf nodes. The main reasons are that data is only available for some of the nodes, that data is available for intermediate nodes rather than for the leaf nodes, or even that the available data is inconsistent. We address these problems by developing a generalisation of the standard bottom-up calculation method in three ways. First, we allow initial attributions of non-leaf nodes. Second, we admit additional relations between attack steps beyond those provided by the underlying attack tree semantics. Third, we support the calculation of an approximative solution in case of inconsistencies. We illustrate our method, which is based on constraint programming, by a comprehensive case study.

Reachability Analysis of Asynchronous Dynamic Pushdown Networks Based on Tree Semantics Approach

<em>ADPN (Asynchronous Dynamic Pushdown Networks) are an abstract model for concurrent programs with recursive procedures and dynamic thread creation. Usually, asynchronous dynamic pushdown networks are described with interleaving semantics, in which the backward analysis is not effective. In order to improve interleaving semantics, tree semantics approach was introduced. This paper extends the tree semantics to ADPN. Because the reachability problem of ADPN is also undecidable, we address the context-bounded reachability problem and provide an algorithm for backward reachability analysis with tree-based semantics Approach.</em>

Mythological Image in Olonkho of the North-Eastern Yakut Tradition: Sacred Tree

The article discusses the problem of studying the North-Eastern tradition of the Yakut epic. This tradition is part of the Northern regional tradition of the Yakuts. At the moment, the problem of studying the Northern regional tradition remains open. The study was based on the works of P. Ergun, V.N. Toporov, L.V. Dmitrieva, I.V. Pukhov, N.V. Emel'yanov, L.N. Semenova and others. The images and semantics of the sacred tree in the Olonkho of the North-Eastern tradition are considered in detail. This image is characteristic for the 8 texts of the 14 considered Olonkho from momskiy, verkhoyanskiy, abyiskiy and srednekolymskiy districts or Sakha (Yakutia) Republic local traditions. In Olonkho texts of studied tradition the sacred larch image is widespread. As the researchers note, the sacred larch image is the most archaic. Carried out a comparative analysis of the sacred tree in Olonkho from three traditions (Vilyui, Central and North-Eastern). The sacred tree descriptions in the three traditions had their own regional differences. As a result of sacred tree semantics comparison in Olonkho of three traditions had been revealed the following. In the Central tradition, the sacred tree does not reach the Upper and the Lower worlds. In the Vilyui tradition, the tree penetrates through the Middle world and reaches the Upper world, becomes the horse standing for the Supreme deity Urung Ayý toyon ‘White Creator Lord’. In Olonkho of the studied tradition the top of the sacred tree goes to the Upper world and roots penetrate deep into the Lower world. In the middle world the tree Al Luk Mas appears as a center of the world and a sacred place. In the Lower world the sacred tree appears as a hook for the things of its Lord Arsan Tolaya. The main results of the work allows to suggest that the sacred tree semantics in the Olonkho of this tradition is more interesting and distinctive from the Olonkho of other regional traditions.

Stochastic-based Semantics Of Attack-Defense Trees For Security Assessment

Losses caused by cyber-attacks are considerably increasing each year. The need for an optimal security assessment methodology that combines mathematical foundations with practical and user-friendly representations has become imperatively crucial. In this paper, we propose a stochastic security assessment methodology that adopts attack-defense trees model to represent security scenarios, and stochastic models to perform both qualitative and quantitative assessment. We illustrate our approach with a simple but realistic example study.

Quantified CTL: Expressiveness and Complexity

While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic Second-Order Logic for both semantics) and characterise the complexity of its model-checking and satisfiability problems, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy).

Flexible Disambiguation and Expressive Completeness in Dependency Tree Semantics

This paper proposes an extension of Dependency Tree Semantics (DTS), an underspecified formalism originally proposed in Robaldo (2007). The crucial advantage of DTS as compared to other contemporary proposals is its ability to represent Independent Set (IS) readings (a.k.a. scopeless readings), e.g. cumulative and collective readings. DTS achieves the expressivity needed to represent IS readings because it underspecifies Skolem-like functional dependencies. This paper extends DTS by introducing additional meta-constraints in First-Order Logic dedicated to disambiguating underspecified structures. However, it is worth noting that the meta-constraints are independent from DTS, and could be easily re-implemented in any underspecified theory. The meta-constraints achieve flexible disambiguation, in the sense that they allow ambiguous structures to be specified independently of the linguistic (rather than logical) knowledge used. Secondly, DTS, equipped with the meta-constraints, becomes an expressively complete formalism in the sense of Ebert (2005). Expressive completeness is a desirable property for an underspecified formalism, because it allows a representation for each possible subset of available readings.

Subjective auxiliary state for coarse-grained concurrency

From Owicki-Gries' Resource Invariants and Jones' Rely/Guarantee to modern variants based on Separation Logic, axiomatic logics for concurrency require auxiliary state to explicitly relate the effect of all threads to the global invariant on the shared resource. Unfortunately, auxiliary state gives the proof of an individual thread access to the auxiliaries of all other threads. This makes proofs sensitive to the global context, which prevents local reasoning and compositionality. To tame this historical difficulty of auxiliary state, we propose subjective auxiliary state, whereby each thread is verified using a self view (i.e., the thread's effect on the shared resource) and an other view (i.e., the collective effect of all the other threads). Subjectivity generalizes auxiliary state from stacks and heaps to user-chosen partial commutative monoids, which can eliminate the dependence on the global thread structure. We employ subjectivity to formulate Subjective Concurrent Separation Logic as a combination of subjective auxiliary state and Concurrent Separation Logic. The logic yields simple, compositional proofs of coarse-grained concurrent programs that use auxiliary state, and scales to support higher-order recursive procedures that can themselves fork new threads. We prove the soundness of the logic with a novel denotational semantics of action trees and a definition of safety using rely/guarantee transitions over a large subjective footprint. We have mechanized the denotational semantics, logic, metatheory, and a number of examples by a shallow embedding in Coq.

Highlights in infinitary rewriting and lambda calculus

We present some highlights from the emerging theory of infinitary rewriting, both for first-order term rewriting systems and λ-calculus.In the first section we introduce the framework of infinitary rewriting for first-order rewrite systems, so without bound variables. We present a recent observation concerning the continuity of infinitary rewriting.In the second section we present an excursion to the infinitary λ-calculus. After the main definitions, we mention a recent observation about infinite looping λ-terms, that is, terms that reduce in one step to themselves. Next we describe the fundamental trichotomy in the semantics of λ-calculus: Böhm trees, Lévy–Longo trees, and Berarducci trees. We conclude with a short description of a new refinement of Böhm tree semantics, called clocked semantics.

Automatic Test Cases Generation for Statechart Specifications from Semantics to Algorithm

This paper studies automatic test cases generation for Statechart specifications. Applying Tretmans’ approach to generate test cases from labeled transition systems, we provide a solid mathematical basis for conformance testing and automatic test case generation for Statechart specifications. In order to make the test cases generation process more simple and efficient, we propose observable semantics as a suitable semantics model for describing observable behavior subset of a Statechart specification, which is different from complete semantics used for Statechart specification verification and model checking. Then we describe how to use this semantics model for not only generation reactive systems but also critical reactive systems. We also propose a formal conformance relation based on presented semantics model and test hypothesis, and provide an algorithm which, for a Statechart specification, generates a test suite. For Statechart specifications with graph semantics the algorithm can generate complete test suite, and for Statechart specifications with tree semantics cost-efficient sound test suite can be generated.

Moment/History Duality in Prior’s Logics of Branching-Time

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories.

Augmenting branching temporal logics with existential quantification over atomic propositions

In temporal-logic model checking, we verify the correctness of a program with respect to a desired behavior by checking whether a structure that models the program satisfies a temporal logic formula that specifies this behavior. One of the ways to overcome the expressiveness limitation of temporal logics is to augment them with quantification over atomic propositions. In this paper we consider the extension of branching temporal logics with existential quantification over atomic propositions. Once we add existential quantification to a branching temporal logic, it becomes sensitive to unwinding. That is, unwinding a structure into an infinite tree does not preserve the set of formulas it satisfies. Accordingly, we distinguish between two semantics, two practices as specification languages, and two versions of the model-checking problem for such a logic. One semantics refers to the structure that models the program, and the second semantics refers to the infinite computation tree that the program induces. We examine the complexity of the model-checking problem in the two semantics for the logics CTL and CTL* augmented with existential quantification over atomic propositions. Following the cheerless results that we get, we examine also the program complexity of model checking; i.e., the complexity of this problem in terms of the program, assuming the formula is fixed. We show that while fixing the formula dramatically reduces model-checking complexity in the tree semantics, its influence on the structure semantics is poor.

An Extended Branching-Time Ockhamist Temporal Logic

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated ’’restricted variables‘‘ called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time. We construct an axiomatic system for this extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc.