True Formula Research Articles

DECLAREd: A Polytime LTLf Fragment

This paper considers a specification rewriting meachanism for a specific fragment of Linear Temporal Logic for Finite traces, DECLAREd, working through an equational logic and rewriting mechanism under customary practitioner assumptions from the Business Process Management literature. By rewriting the specification into an equivalent formula which might be easier to compute, we aim to streamline current state-of-the-art temporal artificial intelligence algorithms working on temporal logic. As this specification rewriting mechanism is ultimately also able to determine with the provided specification is a tautology (always true formula) or a formula containing a temporal contradiction, by detecting the necessity of a specific activity label to be both present and absent within a log, this implies that the proved mechanism is ultimately a SAT-solver for DECLAREd. We prove for the first time, to the best of our knowledge, that this fragment is a polytime fragment of LTLf, while all the previously-investigated fragments or extensions of such a language were in polyspace. We test these considerations over formal synthesis (Lydia), SAT-Solvers (AALTAF) and formal verification (KnoBAB) algorithms, where formal verification can be also run on top of a relational database and can be therefore expressed in terms of relational query answering. We show that all these benefit from the aforementioned assumptions, as running their tasks over a rewritten equivalent specification will improve their running times, thus motivating the pressing need of this approach for practical temporal artificial intelligence scenarios. We validate such claims by testing such algorithms over a Cybersecurity dataset.

Fuzzy logics – quantitatively

ABSTRACT The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length built with exactly one variable. Then, we investigate such proportion for satisfiable formulas. Second, we generalise our investigation on formulas written with k ≥ 1 variables. The primary goal of the paper is the research on the asymptotic behaviour of these fractions when the length n tends to infinity. If such limits exists, they are real numbers between 0 and 1, which are called the density of truth or the density of SAT. To compare the density of truth and the density of satisfiable formulas for both fragments of 3-valued Gödel–Dummett's and Łukasiewicz's logics we use the powerful theory of analytic combinatorics. This paper is a natural continuation of the previous brief conference note by Kostrzycka and Zaionc (2020) as well as enriched with some previous results from Kostrzycka and Zaionc (2003). In the conference note we computed analytically the density of truth and the density of SAT (with a determined precision) for 3-valued Łukasiewicz's logic restricted to a language with only one variable. In Kostrzycka and Zaionc (2003) we computed the same values for exactly the same fragment of the 3-valued Gödel–Dummett logic. This paper answers the more general questions of the existence of density of truth and density of SAT for both many-valued logics with an arbitrary finite number of variables. Therefore this paper gives an an interesting picture of two main families of finite-valued fuzzy logics problems treated quantitatively. This picture is taken from the perspective of classical logic. It shows that unexpectedly there is quantitatively a little distance between these two approaches.

The Pleasures of Unpleasure: Jacques Lacan and the Atheism Beyond the “Death of God”

Although the desire to be free from God springs from humanity’s wish to enjoy pleasure without restraint, Lacan observes that humans remain neurotic and unhappy. That is because the prevailing “dead of God” form of atheism relies on the denial of a father/god, a negation that inadvertently replicates the logic of religion. Lacan, by contrast, grounds his atheism in a theory of pleasure that recognizes the role of “unpleasure” in breaking the tedium of easy, unlimited gratification. Turning to Greek tragedy, Lacan shows how the ancient world used the gods as creators of “unpleasure” to generate human jouissance. The figure of Antigone, in particular, shows how the divine function can fulfill “the true formula of atheism,” which is not “God is dead,” but rather, Lacan affirms, that “God is unconscious.”

What is the true formula for soil permeability? Not clear

What is the true formula for soil permeability? Not clear

Set-theoretic reflection is equivalent to induction over well-founded classes

We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The equivalence is proved in primitive recursive set theory (which is weaker than Kripke-Platek set theory) extended by the axiom of dependent choice.

Model Mis-Specification in Newsvendor Decisions: A Comparison of Frequentist Parametric, Bayesian Parametric and Nonparametric Approaches

We compare three different approaches studied by past literature on data-driven inventory optimization--- Frequentist Parametric (FP), Bayesian Parametric (BP) and Nonparametric--- for the newsvendor problem. For the Parametric approaches, we allow for mis-specification of the demand model. We prove, under mild regularity conditions, (i) asymptotic bias and variance formulas of FP and BP are equivalent, (ii) mis-specified Parametric approaches yield asymptotically biased decisions, unlike the correctly-specified Parametric approaches and the Nonparametric approach, and (iii) asymptotic variance of the mis-specified Parametric approaches converges to zero at rate $1/n$, in contrast to the $1/n^2$ rate for the correctly-specified Parametric approaches and the Nonparametric approach, where $n$ is the number of demand samples. We then show, for nine pairs of assumed versus true demand distribution pairs, (iv) asymptotic bias and variance formulas approximate finite-sample counterparts very well, (v) correctly-specified Parametric approaches dominate the Nonparametric approach in the asymptotic mean-squared error (AMSE) of the decision and the cost, and (vi) surprisingly, it is possible for mis-specified Parametric approaches to dominate the Nonparametric approach in the AMSE of the decision and the cost. We compare the approaches on a dataset from a large fresh food chain, and discuss the nuances of choosing the ``best'' approach.

Partial Awareness

We develop a modal logic to capture partial awareness. The logic has three building blocks: objects, properties, and concepts. Properties are unary predicates on objects; concepts are Boolean combinations of properties. We take an agent to be partially aware of a concept if she is aware of the concept without being aware of the properties that define it. The logic allows for quantification over objects and properties, so that the agent can reason about her own unawareness. We then apply the logic to contracts, which we view as syntactic objects that dictate outcomes based on the truth of formulas. We show that when agents are unaware of some relevant properties, referencing concepts that agents are only partially aware of can improve welfare.

Axiomatic and dual systems for constructive necessity, a formally verified equivalence

ABSTRACTWe present a proof of the equivalence between two deductive systems for constructive necessity, namely an axiomatic characterisation inspired by Hakli and Negri's system of derivations from assumptions for modal logic , a Hilbert-style formalism designed to ensure the validity of the deduction theorem, and the judgmental reconstruction given by Pfenning and Davies by means of a natural deduction approach that makes a distinction between valid and true formulae, constructively. Both systems and the proof of their equivalence are formally verified using the state-of-the-art proof assistant Coq. The proof approach taken throughout the paper unveils the use of some alternative proof methods that allow for a smooth transition from the high-level mathematical proofs to their mechanised counterparts.

Structure evolution of mononuclear tungsten and molybdenum species in the protonation process: Insight from FPMD and DFT calculations

In this work, we apply static density functional theory (DFT) calculations, as well as classical and first-principles molecular dynamics (FPMD) simulations, using the free-energy perturbation method to study the protonation ability, active site and structures of W(VI) and Mo(VI) in acidic aqueous solution. Using FPMD simulations, utilizing the pKa's calculation technique, we concluded that the octahedral WO2(OH)2(H2O)2 is the true formula for tungstic acid (H2WO4), and the hydroxyl ligands are the acidic site. This aqueous structure of H2WO4 is analogous to the previously reported structure of molybdic acid (H2MoO4). The FPMD trajectories of the tungstic acid deprotonation show that the mono-protonated monotungstate ion (HWO4−) may partially exist as a five-coordinated WO3(OH)(H2O)− species except for the four-coordinated WO3(OH)− species. This result is supported by DFT calculations, with an isoenergetic point (ΔE = 1.9 kcal·mol−1) for the WO3(OH)(H2O)− and WO3(OH)− species, when explicit solvent molecules are taken into account. In contrast, for the H2MoO4 acid, FPMD trajectories during the deprotonation process show that two H2O ligands immediately escape from the first coordinated sphere of Mo(VI) to form the four-coordinated MoO3(OH)− species. This difference indicates that structural expansion of W(VI) began in the first protonated step, while that of Mo(VI) only occurs in the second step. In addition, our calculated first and second acid constants for tungstic acid are higher than previously reported values for molybdic acid. This result suggests that WO42− is more easily protonated than the MoO42− anion in the same acidic solution, which is further confirmed by DFT calculations of hydrated oxoanions and its protonated species, based upon the hydration energy.

The Conditions of Formation of Socio-psychological Competence to Critical Situations at Training of Specialists for Underground Construction

The authors consider innovative materials and structures developed by Boris Biryukov, a Russian researcher, within the framework of structural mechanics and civil engineering. The authors analyze the contribution made by Boris Vladimirovich Biryukov, an outstanding Russian logician, into the development of applied logic in Russia. In 1962 – 1991, Boris Biryukov headed the methodology department of the Cybernetics Research Council at the USSR Academy of Sciences. In some of his works, Biryukov interpreted the ideas initially expressed by N.M. Gersevanov, V.I. Shestakov, P. Erenfest and other logicians and mathematicians, who applied the methods, originally developed within the framework of exact and natural sciences, to technology-related problems of the national economy. The authors prove that Boris Biryukov and his colleagues were the first scholars who drew the attention of the research community to the logic-based research performed by N.M. Gersevanov, a prominent engineer and urban developer. In his works, Biryukov proved that this founder of the Russian school of soil mechanics was the first researcher who applied the instruments of mathematical logic to civil engineering problems. In the second part of the article, the authors demonstrate the way V.I. Shestakov developed several Gersevanov's ideas. Finally, the authors offer a sample relay contact circuit applied to the identically true formula compiled according to the rules of the logic of sentential calculus.

The Problem of Using Logic in Structural Mechanics and Electrical Engineering as Viewed by the Russian Researcher Boris Biryukov

The authors consider innovative materials and structures developed by Boris Biryukov, a Russian researcher, within the framework of structural mechanics and civil engineering. The authors analyze the contribution made by Boris Vladimirovich Biryukov, an outstanding Russian logician, into the development of applied logic in Russia. In 1962 – 1991, Boris Biryukov headed the methodology department of the Cybernetics Research Council at the USSR Academy of Sciences. In some of his works, Biryukov interpreted the ideas initially expressed by N.M. Gersevanov, V.I. Shestakov, P. Erenfest and other logicians and mathematicians, who applied the methods, originally developed within the framework of exact and natural sciences, to technology-related problems of the national economy. The authors prove that Boris Biryukov and his colleagues were the first scholars who drew the attention of the research community to the logic-based research performed by N.M. Gersevanov, a prominent engineer and urban developer. In his works, Biryukov proved that this founder of the Russian school of soil mechanics was the first researcher who applied the instruments of mathematical logic to civil engineering problems. In the second part of the article, the authors demonstrate the way V.I. Shestakov developed several Gersevanov's ideas. Finally, the authors offer a sample relay contact circuit applied to the identically true formula compiled according to the rules of the logic of sentential calculus.

A vibrational spectroscopic study of the silicate mineral normandite – NaCa(Mn2+,Fe2+)(Ti,Nb,Zr)Si2O7(O,F)2

We have studied the mineral normandite using a combination of scanning electron microscopy with energy dispersive spectroscopy and vibrational spectroscopy.The mineral normandite NaCa(Mn2+,Fe2+)(Ti,Nb,Zr)Si2O7(O,F)2 is a crystalline sodium calcium silicate which contains rare earth elements. Chemical analysis shows the mineral contains a range of elements including Na, Mn2+, Ca, Fe2+ and the rare earth element niobium. No Raman bands are observed above 1100cm−1. The mineral is characterised by Raman bands observed at 724, 748, 782 and 813cm−1. Infrared bands are broad; nevertheless bands may be resolved at 723, 860, 910, 958, 933, 1057 and 1073cm−1. Intense Raman bands at 454, 477 and 513cm−1 are attributed to OSiO bending modes. No Raman bands are observed in the hydroxyl stretching region, but low intensity infrared bands are observed at 3191 and 3450cm−1. This observation brings into question the true formula of the mineral.

A method to calculate the acetabular cup anteversion after total hip replacement based on 3D coordinate system

Aim: To explore an accurate method to calculate acetabular cup anteversion after total hip arthroplasty. Method: 1) A 3D coordinate system was established with the center of the hip joint rotation center base as coordinate center. The acetabular exit plane and Pettersson formula acetabular anteversion and Riten Pradhan formula acetabular anteversion and acetabular true anteversion were drawn; 2) Determine the mathematical expression of Pettersson formula acetabular anteversion α and Riten Pradhan formula acetabular anteversion β in the coordinate system. The true acetabular anteversion is projection angle of Pettersson formula acetabular anteversion α on cross-section in the presence of acetabular abduction δ, determining mathematical expression of the acetabular anteversion θ by trigonometric functions. Results: Real acetabular cup anteversion θ = arctg (tgβ/cosδ). Conclusion: The true acetabular cup anteversion and Pettersson formula anteversion and Riten Pradhan for mula anteversion were quite different. The difference was increased with the acetabular cup abduction angle increased. The formula was simple and accurate and worthy of clinical reference.

Volitional Control of Cortical Oscillations and Synchrony

Oscillatory activity in motor cortex has been observed in many experimental contexts, leading to various hypotheses about its possible behavioral function. In this issue of Neuron, Engelhard etal. (2013) report that oscillations can be volitionally controlled, opening new directions to explore their function and underlying mechanisms.

Optimal decision procedures for MPNL over finite structures, the natural numbers, and the integers

Interval temporal logics provide a natural framework for qualitative and quantitative temporal reasoning over interval structures, where the truth of formulas is defined over intervals rather than points. In this paper, we study the complexity of the satisfiability problem for Metric Propositional Neighborhood Logic (MPNL). MPNL features two modalities to access intervals “to the left” and “to the right” of the current one, respectively, plus an infinite set of length constraints. MPNL has been recently shown to be decidable over finite linear orders and the natural numbers by a doubly exponential procedure, leaving the tightness of the complexity bound as an open problem. We improve such a result by proving that the satisfiability problem for MPNL over finite linear orders and the natural numbers, as well as over the integers, is actually EXPSPACE-complete, even when length constraints are encoded in binary.

Highly Accurate Chemical Formula Prediction Tool Utilizing High-Resolution Mass Spectra, MS/MS Fragmentation, Heuristic Rules, and Isotope Pattern Matching

Mass spectrometry is commonly applied to qualitatively and quantitatively profile small molecules, such as peptides, metabolites, or lipids. Modern mass spectrometers provide accurate measurements of mass-to-charge ratios of ions, with errors as low as 1 ppm. Even such high mass accuracy, however, is not sufficient to determine the unique chemical formula of each ion, and additional algorithms are necessary. Here we present a universal software tool for predicting chemical formulas from high-resolution mass spectrometry data, developed within the MZmine 2 framework. The tool is based on the use of a combination of heuristic techniques, including MS/MS fragmentation analysis and isotope pattern matching. The performance of the tool was evaluated using a real metabolomic data set obtained with the Orbitrap MS detector. The true formula was correctly determined as the highest-ranking candidate for 79% of the tested compounds. The novel isotope pattern-scoring algorithm outperformed a previously published method in 64% of the tested Orbitrap spectra. The software described in this manuscript is freely available and its source code can be accessed within the MZmine 2 source code repository.

Unified QBF certification and its applications

Quantified Boolean formulae (QBF) allow compact encoding of many decision problems. Their importance motivated the development of fast QBF solvers. Certifying the results of a QBF solver not only ensures correctness, but also enables certain synthesis and verification tasks. To date the certificate of a true formula can be in the form of either a syntactic cube-resolution proof or a semantic Skolem-function model whereas that of a false formula is only in the form of a syntactic clause-resolution proof. The semantic certificate for a false QBF is missing, and the syntactic and semantic certificates are somewhat unrelated. This paper identifies the missing Herbrand-function countermodel for false QBF, and strengthens the connection between syntactic and semantic certificates by showing that, given a true QBF, its Skolem-function model is derivable from its cube-resolution proof of satisfiability as well as from its clause-resolution proof of unsatisfiability under formula negation. Consequently Skolem-function derivation can be decoupled from special Skolemization-based solvers and computed from standard search-based ones. Experimental results show strong benefits of the new method.

The Experimental Film Remake and the Digital Archive Effect: <i>A Movie by Jen Proctor</i> and <i>Man with a Movie Camera: The Global Remake</i>

When we think of film remakes, what come to mind are likely Hollywood narratives reproduced with new stars, more special effects, and bigger budgets, whose producers hope to cash in on a tried and true formula updated to suit the tastes of contemporary audiences. Recently, however, a number of experimental filmmakers have chosen quite different sources to update. Over the past few years filmmakers Jennifer Proctor and Perry Bard have returned to classics of experimental film to these provocative works in and for the digital era. Jennifer Proctor's A Movie by Jen Proctor (US, 2010) uses images from online file-sharing sites to mimic Bruce Conner's classic 1958 experimental film A Movie, while Perry Bard's Man with a Movie Camera: Global Remake (ongoing since 2008) uses online interactive software to allow users worldwide to upload images and participate in a collective, daily remake of Dziga Vertov's seminal 1929 film Man with a Movie Camera. Given that experimental film often encourages the viewer to explore the very experience of viewing a film, these digitally based of experimental films inevitably draw attention not only to how the world that is imaged within them has changed but also to how our experiences of that world through its reproduction as image have been altered by digital media. form of the remake allows us to see both similarity and difference as they emerge across time. As Laura Grindstaffhas noted, writing about the more mainstream form of remake mentioned above, The remake is . . . a rich site for critical analysis precisely because its derivative status, its very and duplicity forces a certain assessment of conventional notions of authorship, authenticity, and originality. On the one hand, the existence of a remake only seems to confirm the fact that originality lies elsewhere-in the prior text. On the other hand, the remake helps expose originality as a relative, not absolute, concept.1 These two shot-for-shot explicitly reveal the fact that their origin lies in an other, prior text; that is precisely their point. More significantly, however, I would argue that these two films in their secondariness point to the relative experience of watching similar images produced through different moving-image media, indicating the ways in which digital media technologies have altered the very conditions of knowledge about the world-both past and present-as it is obtained through images. By appropriating images either from digital archives in A Movie by Jen Proctor or into a digital work in Man with a Movie Camera: Global Remake, these filmmakers draw attention to the ways in which digital media have reshaped both our experience of watching a film-experimental and otherwise-and our experience of the world through its reproduction as images. In this essay, I argue that these two remakes offer an opportunity for us to think through the ways in which digital media produce a mediated experience of the world both similar to and different from the mediated experience of the world produced by filmic images. A Movie by Jen Proctor In 1958, Bruce Conner's A Movie radically disrupted notions of authorship while simultaneously drawing attention to the materiality of the filmic image and performing an incisive critique of the relationship between film images and the spectacle of human violence and destruction. Drawing on previously shot or film footage from a variety of sources, including films commercially produced for the home market, Conner crafted a twelve-minute reflection of the contemporary cinematic unconscious, bringing together pieces of footage-of motorcycle accidents, women undressing, atomic explosions, and a charging elephant, to name only a few-that would likely never have found one another otherwise.2 Fifty-two years later, experimental filmmaker Jennifer Proctor replicated Conner's film in and for the digital era in A Movie by Jen Proctor (2010). …

An Optimal Decision Procedure for MPNL over the Integers

Interval temporal logics provide a natural framework for qualitative and quantitative temporal reason- ing over interval structures, where the truth of formulae is defined over intervals rather than points. In this paper, we study the complexity of the satisfiability problem for Metric Propositional Neigh- borhood Logic (MPNL). MPNL features two modalities to access intervals "to the left" and "to the right" of the current one, respectively, plus an infinite set of length constraints. MPNL, interpreted over the naturals, has been recently shown to be decidable by a doubly exponential procedure. We improve such a result by proving that MPNL is actually EXPSPACE-complete (even when length constraints are encoded in binary), when interpreted over finite structures, the naturals, and the in- tegers, by developing an EXPSPACE decision procedure for MPNL over the integers, which can be easily tailored to finite linear orders and the naturals (EXPSPACE-hardness was already known).

Metric propositional neighborhood logics on natural numbers

Interval logics formalize temporal reasoning on interval structures over linearly (or partially) ordered domains, where time intervals are the primitive ontological entities and truth of formulae is defined relative to time intervals, rather than time points. In this paper, we introduce and study Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is "met by" the current one and to an interval that "meets" the current one, plus an infinite set of length constraints, regarded as atomic propositions, to constrain the length of intervals. We argue that MPNL can be successfully used in different areas of computer science to combine qualitative and quantitative interval temporal reasoning, thus providing a viable alternative to well-established logical frameworks such as Duration Calculus. We show that MPNL is decidable in double exponential time and expressively complete with respect to a well-defined sub-fragment of the two-variable fragment $${{\rm FO}^2[\mathbb{N},=,<,s]}$$ of first-order logic for linear orders with successor function, interpreted over natural numbers. Moreover, we show that MPNL can be extended in a natural way to cover full $${{\rm FO}^2[\mathbb{N},=,<,s]}$$ , but, unexpectedly, the latter (and hence the former) turns out to be undecidable.