Logical Properties Research Articles

$$\textsf{ST}$$ and $$\textsf{TS}$$ as Product and Sum

AbstractThe set of $$\textsf{ST}$$ ST -valid inferences is neither the intersection, nor the union of the sets of $$\textsf{K}_3$$ K 3 -valid and $$\textsf{LP}$$ LP -valid inferences, but despite the proximity to both systems, an extensional characterization of $$\textsf{ST}$$ ST in terms of a natural set-theoretic operation on the sets of $$\textsf{K}_3$$ K 3 -valid and $$\textsf{LP}$$ LP -valid inferences is still wanting. In this paper, we show that it is their relational product. Similarly, we prove that the set of $$\textsf{TS}$$ TS -valid inferences can be identified using a dual notion, namely as the relational sum of the sets of $$\textsf{LP}$$ LP -valid and $$\textsf{K}_3$$ K 3 -valid inferences. We discuss links between these results and the interpolation property of classical logic. We also use those results to revisit the duality between $$\textsf{ST}$$ ST and $$\textsf{TS}$$ TS . We present a notion of duality on which $$\textsf{ST}$$ ST and $$\textsf{TS}$$ TS are dual in exactly the same sense in which $$\textsf{LP}$$ LP and $$\textsf{K}_3$$ K 3 are dual to each other.

Towards partial monitoring: Never too early to give in

Runtime Verification is a lightweight formal verification technique used to verify whether a system behaves as expected at runtime. Expected behaviour is typically formally specified using properties, which are used to automatically synthesise monitors. Properties that can be verified at runtime by a monitor are called monitorable, while those that cannot are termed non-monitorable. In this paper, we revisit the notion of monitorability and demonstrate how non-monitorable properties can still be used to generate partial monitors. We tackle this from two different perspectives: (i) by recognising that a monitor can give up on monitoring the property under analysis if it recognises that the monitoring will never conclude the satisfaction or violation of the property; (ii) by recognising that a monitor can give up on events that are not necessary for successful monitoring of the property under analysis. By considering these two aspects, we present how to achieve partial monitoring of Linear Temporal Logic properties by building upon the standard monitor construction. Finally, we present a prototype implementation of our approach and its application to a remote inspection case study, as well as a set of evaluation experiments to stress test our approach using synthetic properties.

Molecular Logic Gates Derived from Fluorescent Natural Products

Fluorescent natural products have been a source of fascination for centuries. In this review, we highlight natural products and natural product derivatives as optical logic-based molecules. The early beginnings of the field of molecular logic-based computation are introduced and followed with literature examples of logic gates from fluorescent natural products. The intention is to arouse the curiosity of readers to go out and discover more fluorescent natural products with intrinsic logic properties.

Analytic and Structural Insights into Eigendecompositions of J2 Binormal Unitary Matrices on the Complex Plane

This research focuses on the eigende compositions of J2 binormal unitary matrices, denoted as J_2^bum (r). These matrices encapsulate matrix components with cohesive logical properties and secondary binormal behavior along a specified unit loop r∈J_2. Addressing gaps in current knowledge, we establish the existence of a decomposition J_2^bum (r)=Un(r)Bi(r)Un(r)^P, meeting conditions such that Un(r)^P=Un(r)^* (conjugate transpose), Bi(r) is a real binormal matrix, and both Un(r) and Bi(r) are analytic functions of a positive integer N. The decomposition extends the well-known Rellich theorem to matrix-valued functions exhibiting J2 binormal unitarity on the real number line. Furthermore, this theorem can be adapted for functions with analyticity and J2 binormal unitary characteristics along lines or circles in the complex plane, and the findings are extended to J2 binormal unitary matrices with elements satisfying a unitary series.

Face-degree-based topological descriptors of germanium phosphide

In graph theory, topological indices are numerical metrics that give information about a graph’s structural traits. The face index is one such topological index that describes planar networks. Since the discovery of graphene, the genealogy of two-dimensional 2D crystals has expanded and currently contains a large variety that has all logical electrical properties required for nano electronics. Nanotechnology benefits from the use of materials that resemble Dirac, such as silicon, graphite, semiconductors, and germanene, as well as TMDC (phosporene), a transition metal dichalcogenide. In contrast with standard topological descriptors, which are numerical values utilised to characterise molecular structures, the face index presents a potentially more comprehensive method for obtaining structural details. In investigations involving quantitative structure-property relationships (QSPR), this may result in more precise predictions. We calculated the recently created face index of Germanium Phosphide (GeP) and its many shapes, including triangle, rhombus, hourglass, and concentric circles.

Which are the true defeasible logics?

The class of defeasible logics is only vaguely defined – it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic DL ( ∂ | | ) introduced new features to such logics, which have repercussions that we explore. In particular, we define a class of logics that accommodates the new logic while retaining the traditional properties of defeasible logics.

On the logical and computational properties of the Vitali covering theorem

We study a version of the Vitali covering theorem, which we call WHBU and which is a direct weakening of the Heine-Borel theorem for uncountable coverings, called HBU. We show that WHBU is central to measure theory by deriving it from various central approximation results related to Littlewood's three principles. A natural question is then how hard it is to prove WHBU (in the sense of Kohlenbach's higher-order Reverse Mathematics), and how hard it is to compute the objects claimed to exist by WHBU (in the sense of Kleene's computation schemes S1-S9). The answer to both questions is ‘extremely hard’, as follows: on one hand, in terms of the usual scale of (conventional) comprehension axioms, WHBU is only provable using Kleene's ∃3, which implies full second-order arithmetic. On the other hand, realisers (aka witnessing functionals) for WHBU, so-called Λ-functionals, are computable from Kleene's ∃3, but not from weaker comprehension functionals. Despite this hardness, we show that WHBU, and certain Λ-functionals, behave much better than HBU and the associated class of realisers, called Θ-functionals. In particular, we identify a specific Λ-functional called ΛS which adds no computational power to the Suslin functional, in contrast to Θ-functionals. Finally, we introduce a hierarchy involving Θ-functionals and HBU.

Output Stabilizing Control of Complex Biological Networks Based on Boolean Algebra Analysis.

Output stabilizing control of biological systems is of utmost importance in systems biology since key phenotypes of biological networks are often encoded by a small subset of their phenotypic marker nodes. This study addresses the challenge of output stabilizing control for complex biological systems modeled by Boolean networks (BNs). The objective is to identify a set of constant control inputs capable of driving the BN toward a desirable long-term behavior with respect to specified output nodes. Leveraging the algebraic properties of Boolean logic, we develop a novel control algorithm that reformulates the output stabilizing control problem into a simple graph theoretic problem involving auxiliary BNs, the scale of which significantly decreases compared to the original BN. The proposed method ensures superiority over previous results in terms of both the number of control inputs and computational loads, since it searches for the solution within the reduced BNs while retaining essential structures needed for output stabilization. The efficacy of the proposed control scheme is demonstrated through extensive numerical experiments with complex random BNs and real biological networks. To support the reproducible research initiative, detailed results of numerical experiments are provided in the supplementary material, and all the implementation codes are made accessible at https://github.com/choonlog/OutputStabilization.

Proof exploration using dynamic geometry systems with integrated automated deduction capabilities

Due to its formal, logical and spatial properties, geometry is well suited for the exploration of new knowledge, new properties that arise from different constructions and new insights into already known constructions, to the exploration of proofs of new conjectures, to the exploration of new proofs of known theorems. With a Dynamic Geometry System (DGS) we get an environment where new conjectures can be easily formulated and visually verified (but not proven). With a Geometry Automated–Theorem–Prover (GATP) we get an environment where conjectures/theorems can be formally proved. We explore some environments where DGS and GATP are combined, analysing their possibilities for the exploration of new conjectures and proofs, having in mind their use in a learning situation.

Are generics quantificational?

The standard view about generic generalizations is that they have a tripartite quantificational logical form involving a phonologically null quantificational expression called ‘Gen’. However, proponents of the cognitive defaults theory of generics have forcefully rejected this view, instead arguing that generics express the default generalizations of our cognitive system, and, as such, they are different in kind from quantificational generalizations. While extant criticism of the cognitive defaults theory has focused on the extent to which it is supported by the empirical evidence, there has been little discussion of a neglected, albeit essential, theoretical argument in its defence, namely, that generics cannot be quantificational because they lack a central logical property of quantifiers: isomorphism invariance. This paper addresses this lacuna by considering and rejecting this argument. Consequently, an essential argument in favour of the cognitive default theory is found wanting.

Strong Backdoors for Default Logic

In this article, we introduce a notion of backdoors to Reiter’s propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor evaluation (parameterised by the size of the given backdoor) for various kinds of target classes (CNF, KROM, MONOTONE) and all SCHAEFER classes. Also, we study generalisations of HORN-formulas, namely QHORN, RHORN, as well as DUALHORN. For these classes, we also classify the computational complexity of the implication problem. We show that backdoor detection is fixed-parameter tractable for the considered target classes and prove a complete trichotomy for backdoor evaluation. The problems are either fixed-parameter tractable, para-DeltaP2-complete, or para-NP-complete, depending on the target class.

Knowledge-based query system for the critical minerals

Critical minerals are increasingly used in advanced, modern technologies. Exploration for these minerals require efficient mechanisms to search for the latest geological knowledge about the petrogenesis and spatial distribution of these essential resources. Although the current text-based deposit classification schemes help geoscientists to understand how and where these critical minerals form, they cannot easily be queried by software without extensive natural language processing and knowledge modeling. Ontologies can explicitly specify the knowledge scattered in the texts and tables of these schemes and the Critical Minerals Mapping Initiative (CMMI) database by way of logical structures whose results can automatically be processed and queried. They can also draw new knowledge by inference from the ones that are explicitly specified in them. These qualities make ontologies a perfect choice for digital knowledge storage, search, and extraction. The Critical Minerals Ontology (CMO) is described herein by reusing the logical class and property structures of the top-level Basic Formal Ontology (BFO) and mid-level Common Core Ontologies (CCO) and Relation Ontology (RO). The CMO formally models the knowledge about the critical mineral systems using the latest deposit classification scheme and the CMMI database schema. The ontology specifies the geochemical and geological processes that operate in various geotectonic environments of mineral systems to form the critical minerals in different deposit types. It models the properties of both the host minerals that contain the rare-earth elements and those that bear other types of elements. The CMO also represents uses of specific critical minerals in the manufacturing of industrial products, their alternate substitutes, and countries that produce, import, and export them. A query system, applying the Python programming language, accesses the knowledge modeled in the CMO and allows users through interactive web pages to query the ontology and extract different types of information from it. The ontology and the query system are useful for research in ore mineralogy and critical mineral prospecting. The information modeled by the ontology and served by the query system allows users to classify their ore specimen data into specific deposit types.

Harnessing large language models for coding, teaching and inclusion to empower research in ecology and evolution

Abstract Large language models (LLMs) are a type of artificial intelligence (AI) that can perform various natural language processing tasks. The adoption of LLMs has become increasingly prominent in scientific writing and analyses because of the availability of free applications such as ChatGPT. This increased use of LLMs not only raises concerns about academic integrity but also presents opportunities for the research community. Here we focus on the opportunities for using LLMs for coding in ecology and evolution. We discuss how LLMs can be used to generate, explain, comment, translate, debug, optimise and test code. We also highlight the importance of writing effective prompts and carefully evaluating the outputs of LLMs. In addition, we draft a possible road map for using such models inclusively and with integrity. LLMs can accelerate the coding process, especially for unfamiliar tasks, and free up time for higher level tasks and creative thinking while increasing efficiency and creative output. LLMs also enhance inclusion by accommodating individuals without coding skills, with limited access to education in coding, or for whom English is not their primary written or spoken language. However, code generated by LLMs is of variable quality and has issues related to mathematics, logic, non‐reproducibility and intellectual property; it can also include mistakes and approximations, especially in novel methods. We highlight the benefits of using LLMs to teach and learn coding, and advocate for guiding students in the appropriate use of AI tools for coding. Despite the ability to assign many coding tasks to LLMs, we also reaffirm the continued importance of teaching coding skills for interpreting LLM‐generated code and to develop critical thinking skills. As editors of MEE, we support—to a limited extent—the transparent, accountable and acknowledged use of LLMs and other AI tools in publications. If LLMs or comparable AI tools (excluding commonly used aids like spell‐checkers, Grammarly and Writefull) are used to produce the work described in a manuscript, there must be a clear statement to that effect in its Methods section, and the corresponding or senior author must take responsibility for any code (or text) generated by the AI platform.

Phrasal Coordination Relatedness Logic

I presented a sub-classical relating logic based on a relating via an NL-inspired relating relation Rcss. The relation Rcss is motivated by the NL-phenomenon of phrasal (subsentential) coordination, exhibiting an important aspect of contents relating among the arguments of binary connectives. The resulting logic Lcss can be viewed as a relevance logic exhibiting a contents related relevance, stronger than the variable-sharing property of other relevance logics like R. Note that relating here is not “tailored” to justify some predetermined logic; rather, the relating relation is independently justified, and induces a logic not previously investigated.

History and A Phytopharmacological Review of Curcuma Amada

Plants are one of the main sources of biologically active materials and crude drugs. Curcuma amada is an plant that belongs to Zingiberaceae family of curcumin. Curcuma amada (Zingiberaceae) basically known as mango ginger because its flavour of rhizome and foliar parts have a similar aroma to mango. It is one of the most important species of Curcuma family having medicinal, traditional and bio- logical properties. The aim of the present review is to know about the phytochemicals, volatile compounds, antimicrobial and other biological activities. Volatile oils extracted from rhizomes of Curcuma amada are rich in phytoconstituents. The curcuminoids present in C.amada is responsible for its therapeutic and biological activities. It is traditionally used to treat various diseases in human being which includes anti-inflammatory, anti-bacterial, anti-cancer, anti-tubercular, anti -allergy, anthelmintic and anti- pyretic activities by their extract. It also possesses healing of various skin disorders. In Ayurveda and Unani systems of medicine have given much importance to mango ginger as an appetizer, alexteric, antipyretic, aphrodisiac, diuretic, emollient, expectorant and laxative and to cure biliousness, itching, skin diseases, bronchitis, asthma, hiccough and inflammation due to injuries. They also used in the manufacture of pickles, chutney, salad and jam.

Algorithmic properties of modal and superintuitionistic logics of monadic predicates over finite Kripke frames

Abstract We show that the monadic fragment of the modal predicate logic of a single Kripke frame with finitely many possible worlds, but possibly infinite domains, is decidable. This holds true even for multimodal logics with equality, regardless of whether equality is interpreted as identity or as congruence. By the Gödel–Tarski translation, similar results follow for superintuitionistic predicate logics, with or without equality. Using these observations, we establish upper algorithmic bounds, which match the known lower bounds, for monadic fragments of some modal predicate logics. In particular, we prove that, if $L$ is a propositional modal logic contained in $\textbf{S5}$, $\textbf{GL.3}$ or $\textbf{Grz.3}$ and the class of finite Kripke frames validating $L$ is recursively enumerable, then the monadic fragment with equality of the predicate logic of finite Kripke frames validating $L$ is $\varPi ^{0}_{1}$-complete; this, in particular, holds if $L$ is one of the following propositional logics: $\textbf{K}$, $\textbf{T}$, $\textbf{D}$, $\textbf{KB}$, $\textbf{KTB}$, $\textbf{K4}$, $\textbf{K4.3}$, $\textbf{S4}$, $\textbf{S4.3}$, $\textbf{GL}$, $\textbf{Grz}$, $\textbf{K5}$, $\textbf{K45}$ and $\textbf{S5}$. We also prove that monadic fragments with equality of logics $\textbf{QAlt}^=_{n}$ and $\textbf{QTAlt}^=_{n}$ are decidable. The obtained results are easily extendable to the multimodal versions of the predicate logics we consider and to logics with the Barcan formula.

Interactive experience of sculpture design based on virtual reality technology

Abstract The application of computer technology provides new ideas for the design of sculpture works. In this paper, with the support of virtual reality technology, the pixel set of each color block is extracted from the actual image to determine the location of the center point of the color block. Based on the extracted information, a visual color marking method is used to realize the 3D registration of the sculpture scene. In the virtual scene, through the virtual modeling of the sculpture work, a spline surface model was generated by applying sparse image sequences and optimally adjusted to transform the surface piece control point problem into a quadratic function of the network vertices. The mathematical logic properties of the virtual reality sculpture work wind direction improved by 22.5 points, the mathematical logic properties of the light design improved by 25.8 points, and the mathematical logic properties of the shadow design improved by 23.1 points. The virtual reality technology provides an interactive experience for the design of sculpture works.

Direct data-driven control with signal temporal logic specifications

Most control synthesis methods under temporal logic properties require a model of the system, however, identifying such a model can be a challenging task. In this work, we develop a direct data-driven control synthesis method for temporal logic specifications, which does not require this explicit modeling step, capable of providing certificates for the general class of linear systems. After collecting a single sequence of input-output data from the system, we synthesize a controller, such that the controlled system satisfies a (possibly unbounded) temporal logic specification. The underlying optimization problem is solved by mixed-integer linear programming. We demonstrate the applicability of the results through simulation examples.

Bounded model checking for interval probabilistic timed graph transformation systems against properties of probabilistic metric temporal graph logic

Cyber-physical systems often encompass complex concurrent behavior with timing constraints and probabilistic failures on demand. The analysis whether such systems with probabilistic timed behavior adhere to a given specification is essential. The formalism of Interval Probabilistic Timed Graph Transformation Systems (IPTGTSs) is often a suitable choice to model cyber-physical systems because (a) its rule-based approach to graph transformation can capture a wide range of system's structure dynamics when the states of the system can be represented by graphs while (b) it employs interval specifications for probabilistic behavior as well as lower and upper bounds on delays of steps to support systems where precise probabilities and delays are not known or may change during the runtime of the system. Probabilistic Metric Temporal Graph Logic (PMTGL) has been introduced as a powerful specification language to express worst-case/best-case probabilistic timed requirements such as actor-based soft deadlines using (a) path properties relying on its Metric Temporal Graph Logic fragment to track individual graph elements and (b) an operator inherited from Probabilistic Timed Computation Tree Logic to express worst-case/best-case probabilistic requirements identifying worst-case/best-case resolutions of non-determinism. Bounded Model Checking (BMC) support for Probabilistic Timed Graph Transformation Systems (PTGTSs) w.r.t. properties specified using PMTGL has been already presented. However, for IPTGTSs no analysis support w.r.t. PMTGL properties has been developed for stating metric temporal properties on identified subgraphs and their structural changes over time.In this paper, we adapt the BMC approach developed for PTGTSs to the case of IPTGTSs extending modeling and analysis support to the usage of probability intervals more appropriately covering cyber-physical systems where probabilistic effects cannot be specified precisely and need to be approximated instead. In our evaluation, we apply an implementation of our BMC approach in AutoGraph to a novel running example demonstrating the effect of using probability intervals instead of precise probability values.

The Implicative Conditional

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. p⇒q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${p\\Rightarrow q}$$\\end{document} is thus defined as ¬◊(p∧¬q)∧◊p∧◊¬q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\lnot } \\Diamond {(p \\wedge \\lnot q) \\wedge } \\Diamond {p \\wedge } \\Diamond {\\lnot q}$$\\end{document}. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut.