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We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem. [ABSTRACT FROM AUTHOR]

AbstractThis paper aims to investigate a class of boundary value problems generated by a third-order differential equation with distributional potentials and some dissipative boundary conditions. We first construct an operator related to the problem, then prove that the operator is dissipative and show some eigenvalue properties of this operator. Further using Krein’s theorem we prove the completeness theorems of the operator. [ABSTRACT FROM AUTHOR]

The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered. [ABSTRACT FROM AUTHOR]

A derivative is a financial asset whose future payoff is a function of underlying assets. Pricing a financial derivative involves setting up a market model, finding a martingale ("fair game") probability measure for the model from the existing asset prices, and using that probability measure to price the derivative. When the number of underlying assets and/or the number of market outcomes in the model is large, pricing can be computationally demanding. In this work, we first formulate the pricing problem in a linear algebra setting, including the realistic setting of incomplete markets where derivatives do not have a unique price. We show that the problem can be solved with a variety of quantum techniques such as quantum linear programming and the quantum linear systems algorithm. While in previous works the martingale measure is assumed to be given, here it is extracted from market variables akin to bootstrapping, a common practice among financial institutions. We discuss the quantum zero-sum game algorithm and the quantum simplex algorithm as viable subroutines. For quantum linear systems solvers, we formalize a new market assumption milder than market completeness, which allows the potential for large speedups. Towards prototype use cases, we conduct numerical experiments motivated by the Black–Scholes–Merton model. [ABSTRACT FROM AUTHOR]

This work provides some information on the eigenvalues and eigenfunctions of a problem which is constructed by a system of equations and symmetric boundary conditions that includes the ordinary second‐order Sturm–Liouville boundary value problem. In particular, we show that the problem has an infinite number of discrete eigenvalues with a greatest lower bound and the corresponding eigenfunctions are complete in mean and energy. We introduce the results using the variational approach that enables us to consider only continuous pair functions instead of absolutely continuous pair functions. [ABSTRACT FROM AUTHOR]

Leibniz algebras are non-antisymmetric generalizations of Lie algebras. In this paper, we investigate the properties of complete Leibniz algebras under certain conditions on their extensions. Additionally, we explore the properties of derivations and direct sums of Leibniz algebras, proving several results analogous to those in Lie algebras. [ABSTRACT FROM AUTHOR]

This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise to a new axiom. Depending on the rule of interpretation, this one changes. With the rule of maximality, one obtains the principle known as disjunctive rationality. With the rule of strong maximality, one obtains the Spohn axiom (also known as the principle of rational monotony, or Lewis' axiom CV). A completeness theorem further substantiates these observations. For interval order, this yields the finite model property and decidability of the calculus. [ABSTRACT FROM AUTHOR]

Let $\mathscr {C}$ be a class of finite and infinite graphs that is closed under induced subgraphs. The well-known Łoś–Tarski Theorem from classical model theory implies that $\mathscr {C}$ is definable in first-order logic by a sentence $\varphi $ if and only if $\mathscr {C}$ has a finite set of forbidden induced finite subgraphs. This result provides a powerful tool to show nontrivial characterizations of graphs of small vertex cover, of bounded tree-depth, of bounded shrub-depth, etc. in terms of forbidden induced finite subgraphs. Furthermore, by the Completeness Theorem, we can compute from $\varphi $ the corresponding forbidden induced subgraphs. This machinery fails on finite graphs as shown by our results: – There is a class $\mathscr {C}$ of finite graphs that is definable in first-order logic and closed under induced subgraphs but has no finite set of forbidden induced subgraphs. – Even if we only consider classes $\mathscr {C}$ of finite graphs that can be characterized by a finite set of forbidden induced subgraphs, such a characterization cannot be computed from a first-order sentence $\varphi $ that defines $\mathscr {C}$ and the size of the characterization cannot be bounded by $f(|\varphi |)$ for any computable function f. Besides their importance in graph theory, the above results also significantly strengthen similar known theorems for arbitrary structures. [ABSTRACT FROM AUTHOR]

Weakly supervised temporal action localization (WTAL) aims to classify and localize actions in untrimmed videos with only video-level labels. Recent studies have attempted to obtain more accurate temporal boundaries by exploiting latent action instances in ambiguous snippets or propagating representative action features. However, empirically handcrafted ambiguous snippet extraction and the imprecise alignment of representative snippet propagation lead to challenges in modeling the completeness of actions for these methods. In this article, we propose a Discriminative Action Snippet Propagation Network (DASP-Net) to accurately discover ambiguous snippets in videos and propagate discriminative instance-level features throughout the video for improving action completeness. Specifically, we introduce a novel discriminative feature propagation module for capturing the global contextual attention and propagating the action concept across the whole video by perceiving the discriminative action snippets with instance information from the same video. Simultaneously, we incorporate denoised pseudo-labels as supervision, where we correct the controversial prediction based on the feature space distribution during training, thereby alleviating false detection caused by noise background features. Furthermore, we design an ambiguous feature mining module, which maximizes the feature affinity information of action and background in ambiguous snippets to generate more accurate latent action and background snippets and learns more precise action instance boundaries through contrastive learning of action and background snippets. Extensive experiments show that DASP-Net achieves state-of-the-art results on THUMOS14 and ActivityNet1.2 datasets. [ABSTRACT FROM AUTHOR]

The logic of bringing-it-about (BIAT) aims to capture a notion of agency in which actions are analysed in terms of their results: 'An agent does something' means that the agent brings it about that something takes place. Our starting point is the basic BIAT logic as introduced by Elgesem in the '90s: this logic contains only a modal operator to express BIAT statements by single agents. Several extensions have been proposed by Elgesem himself and others, notably with the capability operator, coalitions of agents and means-end BIAT statements (i.e. of the form 'the agent does B by doing A'). We first propose a variant of the neighbourhood semantics, called bi-neighbourhood semantics, for the basic BIAT logic and the mentioned extensions, in which a world is equipped by a set of pairs or neighbourhoods. Differently from the semantics defined in the literature, this reformulation is well suited for countermodel construction. We then introduce modular hypersequent calculi for all logics considered in this work. Our calculi enjoy the fundamental property of cut admissibility, from which it follows their completeness with respect to the axiomatization. Moreover, our calculi provide at the same time a decision procedure, as well as the first practical countermodel extraction procedure: from a single failed proof it is possible to build directly a finite countermodel of the formula under verification in the bi-neighbourhood semantics. By this last result, we obtain constructive proofs of the semantic completeness of the calculi and consequently of the finite model property for all logics. [ABSTRACT FROM AUTHOR]

Under study is the Tricomi–Neumann problem for a three-dimensional mixed-type equation with three singular coefficients in a mixed domain consisting of a quarter of a cylinder and a triangular straight prism. We prove the unique solvability of the problem in the class of regular solutions by using the separation of variables in the hyperbolic part of the mixed domain, which yields the eigenvalue problems for one-dimensional and two-dimensional equations. Finding the eigenfunctions of the problems, we use the formula of the solution of the Cauchy–Goursat problem to construct a solution to the two-dimensional problem. In result, we find the solutions to eigenvalue problems for the three-dimensional equation in the hyperbolic part. Using the eigenfunctions and the gluing condition, we derive a nonlocal problem in the elliptic part of the mixed domain. To solve the problem in the elliptic part, we reformulate the problem in the cylindrical coordinate system and separating the variables leads to the eigenvalue problems for two ordinary differential equations. We prove a uniqueness theorem by using the completeness property of the systems of eigenfunctions of these problems and construct the solution to the problem as the sum of a double series. Justifying the uniform convergence of the series relies on some asymptotic estimates for the Bessel functions of the real and imaginary arguments. These estimates for each summand of the series made it possible to prove the convergence of the series and its derivatives up to the second order, as well as establish the existence theorem in the class of regular solutions. [ABSTRACT FROM AUTHOR]

Recent studies have focused on autonomous agents that select their own goals and then select actions to achieve these goals, using online Goal Reasoning (GR). GR agents can revise goals and plans at execution time if unexpected outcomes occur. However, for ethical or legal agent design, even the partial execution of an online plan may result in foreseeable norm violations. To prevent these violations, it is crucial to incorporate GR already at the planning phase. To this end, we design an offline GR system that can harbour normative systems or deontic logics for goal generation. Our main results include a characterization and comparison of the completeness classes for a variety of offline GR planners, and a discussion of the irreducibility of offline GR to pure planning methods. [ABSTRACT FROM AUTHOR]

We show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness results for various computational problems. We exhibit several families of complete problems which can be used for future completeness results in the real hierarchy. As an application we sharpen some results by Bürgisser and Cucker on the complexity of properties of semialgebraic sets, including the Hausdorff distance problem also studied by Jungeblut, Kleist, and Miltzow. [ABSTRACT FROM AUTHOR]

A many-valued modal logic, called linear abelian modal logic LK(A) is introduced as an extension of the abelian modal logic K(A). Abelian modal logic K(A) is the minimal modal extension of the logic of lattice-ordered abelian groups. The logic LK(A) is axiomatized by extending K(A) with the modal axiom schemas □(φ ∨ ψ) → (□φ ∨ □ψ) and (□φ ∧ □ψ) → □(φ ∧ ψ). Completeness theorem with respect to algebraic semantics and a hypersequent calculus admitting cut-elimination are established. Finally, the correspondence between hypersequent calculi and axiomatization is investigated. [ABSTRACT FROM AUTHOR]

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or "associational") languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. [ABSTRACT FROM AUTHOR]

We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we give a characterisation of Esakia spaces dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, DNA -logics and dependence logic. [ABSTRACT FROM AUTHOR]

A short review is presented of results on the spectral theory of arbitrary-order ordinary differential operators with nonintegrable regular singularities. We establish properties of spectral characteristics, prove theorems on completeness of root functions in the corresponding spaces, prove expansion and equiconvergence theorems, and provide a solution of the inverse spectral problem for this class of operators. [ABSTRACT FROM AUTHOR]

[Display omitted] • Estimates of skeletal completeness currently reflect unknown assumptions. • Methods to calculate skeletal completeness are either not being used or not cited. • Typically estimates are not more precise with more years of skeletal experience. • Practitioners demonstrate more agreement for individual bones versus assemblages. • Bones are reported as less complete by practitioners with more experience. Forensic anthropologists engage with numerous and diverse stakeholders in their casework. Regarding the recovery of human remains, these stakeholders may be interested in quantifying or qualifying the amount of remains recovered. How forensic anthropologists respond to such questions, whether verbally or in written reporting, has the potential to impact the trajectory of a case. However, communications about skeletal completeness are rarely discussed within the field. Current data-collection procedures recommend the use of inventories. This approach may be less feasible for complicated assemblages involving commingling or high degrees of fragmentation. Numerous methods exist to quantify the amount of skeletal remains present in complex or larger assemblages, but it remains unclear to what extent forensic anthropologists utilize these methods and whether factors like degree of expertise influence analysts' ability to report skeletal completeness consistently and precisely. A study was designed to examine differences between public and professional perceptions of skeletal completeness, presenting images of incomplete bones and skeletal remains. Survey participants were asked to assess the completeness of the remains in each image. Few patterns were observed regarding photographs of skeletal assemblages, but distinct differences were observed among individual bones between respondents with different degrees of expertise. These responses reflect potentially unexamined assumptions underlying assessments of incomplete bones and skeletal assemblages. This highlights the necessity of standardizing how we report estimates of completeness within the forensic anthropology community and how we discuss these results with external stakeholders. Completeness estimates must be either removed from reports and bench notes or annotated and cited clearly, as is standard with other aspects of forensic anthropological analysis. Several methods are summarized, with recommendations for integrating them into casework. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to summarize and share the field experiment results of KEPCO's project consortium to create a TSO-DSO-DERA interaction scheme. The field experiment was conducted based on the prequalification algorithm proposed in previous research from the same consortium, and was designed to verify the validity of the algorithm under realistic grid conditions. In addition, during the course of the field experiment, it was found that points that were missed or not given much importance in the existing prequalification algorithm could affect the completeness of the overall system, and then practical improvements were made to improve this. The demonstration results confirm that the proposed algorithm is effective in real-world grid environments and can help DSOs to ensure the reliability of the distribution system while supporting DERA's participation in the wholesale market using the proposed prequalification scheme. [ABSTRACT FROM AUTHOR]

This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson's paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven. [ABSTRACT FROM AUTHOR]

This paper has features of mixed nature. It contains new results, in particular, on semitopological groups. We also pose some problems, introduce new definitions and describe in details certain techniques we need below, providing the proofs of not so well-known theorems for the sake of completeness. Hence, this article can be treated also as a kind of a short survey. [ABSTRACT FROM AUTHOR]

This paper will develop ideas from [ 44 ]. We will generalize their work in two directions. First, we provide axioms for justification logics over the base logic B and show that the logic permits a proof of the internalization theorem. Second, we provide alternative frames that more closely resemble the standard versions of the ternary relational frames, as well as a more general approach to the completeness proof. We prove that soundness and completeness hold for justification logics over a wide variety of base logics. Finally, we will strengthen Belnap's variable sharing for the justification logic context, demonstrating that the justifications are properly relevant justifications. [ABSTRACT FROM AUTHOR]

Within the de Sitter ambient space framework, the two different bases of the one-particle Hilbert space of the de Sitter group algebra are presented for the scalar case. Using field operator algebra and its Fock space construction in this formalism, we discuss the existence of asymptotic states in de Sitter QFT under an extension of the adiabatic hypothesis and prove the Fock space completeness theorem for the massive scalar field. We define the quantum state in the limit of future and past infinity on the de Sitter hyperboloid in an observer-independent way. These results allow us to examine the existence of the S-matrix operator for de Sitter QFT in ambient space formalism, a question which is usually obscure in spacetime with a cosmological event horizon for a specific observer. Some similarities and differences between QFT in Minkowski and de Sitter spaces are discussed. [ABSTRACT FROM AUTHOR]

In the current paper we provide a proof of NP-completeness for the Cell Formation Problem (CFP) with the fractional grouping efficacy objective function. First the CFP with a linear objective function is considered. Following the ideas of Pinheiro et al. (2016) we show that it is equivalent to the Bicluster Graph Editing Problem (BGEP), which is known to be NP-complete due to the reduction from the 3-Exact 3-Cover Problem – 3E3CP (Amit, 2004). Then we suggest a polynomial reduction of the CFP with the linear objective to the CFP with the grouping efficacy objective. It proves the NP-completeness of this fractional CFP formulation. Along with the NP-status our paper presents important connections of the CFP with the BGEP and 3E3CP. Such connections could be used for "transferring" of known theoretical properties, efficient algorithms, polynomial cases, and other features of well-studied graph editing and exact covering problems to the CFP. [ABSTRACT FROM AUTHOR]

We study the computational complexity of the universal theory of residuated ordered groupoids, which are algebraic structures corresponding to Nonassociative Lambek Calculus. We prove that the universal theory is co NP -complete which, as we observe, is the lowest possible complexity for a universal theory of a non-trivial class of structures. The universal theories of the classes of unital and integral residuated ordered groupoids are also shown to be co NP -complete. We also prove the co NP -completeness of the universal theory of classes of residuated algebras, algebraic structures corresponding to Generalized Lambek Calculus. [ABSTRACT FROM AUTHOR]

Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson's constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved. [ABSTRACT FROM AUTHOR]

Weakly-supervised temporal action localization (W-TAL) is to locate the boundaries of action instances and classify them in an untrimmed video, which is a challenging task due to only video-level labels during training. Existing methods mainly focus on the most discriminative action snippets of a video by using top-k multiple instance learning (MIL), and ignore the usage of less discriminative action snippets and non-action snippets. This makes the localization performance improve limitedly. In order to mine the less discriminative action snippets and distinguish the non-action snippets better in a video, a novel method based on deep cascaded action attention network is proposed. In this method, the deep cascaded action attention mechanism is presented to model not only the most discriminative action snippets, but also different levels of less discriminative action snippets by introducing threshold erasing, which ensures the completeness of action instances. Besides, the entropy loss for non-action is introduced to restrict the activations of non-action snippets for all action categories, which are generated by aggregating the bottom-k activation scores along the temporal dimension. Thereby, the action snippets can be distinguished from non-action snippets better, which is beneficial to the separation of action and non-action snippets and enables the action instances more accurate. Ultimately, our method can facilitate more precise action localization. Extensive experiments conducted on THUMOS14 and ActivityNet1.3 datasets show that our method outperforms state-of-the-art methods at several t-IoU thresholds. [ABSTRACT FROM AUTHOR]

Accurate quantification of the signal-to-noise ratio (SNR) of a given observational phenomenon is central to associated calculations of sensitivity, yield, completeness, and occurrence rate. Within the field of exoplanets, the SNR of a transit has been widely assumed to be the formula that one would obtain by assuming a boxcar light curve, yielding an SNR of the form |$(\delta /\sigma _0) \sqrt{D}$|⁠. In this work, a general framework is outlined for calculating the SNR of any analytic function and it is applied to the specific case of a trapezoidal transit as a demonstration. By refining the approximation from boxcar to trapezoid, an improved SNR equation is obtained that takes the form |$(\delta /\sigma _0) \sqrt{(T_{14}+2T_{23})/3}$|⁠. A solution is also derived for the case of a trapezoid convolved with a top-hat, corresponding to observations with finite integration time, where it is proved that SNR is a monotonically decreasing function of integration time. As a rule of thumb, integration times exceeding T 14/3 lead to a 10 per cent loss in SNR. This work establishes that the boxcar transit is approximate and it is argued that efforts to calculate accurate completeness maps or occurrence rate statistics should either use the refined expression, or even better numerically solve for the SNR of a more physically complete transit model. [ABSTRACT FROM AUTHOR]

The Arslanov completeness criterion says that a c.e. set A is Turing complete if and only there exists an A-computable function f without fixed points, i.e. a function f such that W f (x) ≠ W x for each integer x. Recently, Barendregt and Terwijn proved that the completeness criterion remains true if we replace the Gödel numbering x ↦ W x with an arbitrary precomplete computable numbering. In this paper, we prove criteria for noncomputability and highness of c.e. sets in terms of (pre)complete computable numberings and fixed point properties. We also find some precomplete and weakly precomplete numberings of arbitrary families computable relative to Turing complete and non-computable c.e. oracles respectively. [ABSTRACT FROM AUTHOR]

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz's 1973 paper 'Towards a foundation of a general proof theory' and refined by Schroeder-Heister in 'Validity concepts in proof-theoretic semantics' (2006). We will call the new notion generalized proof-theoretic validity and show that the logic of generalized proof-theoretic validity is intuitionistic logic. [ABSTRACT FROM AUTHOR]

Formula-based specification of large quasigroups with the use of complete mappings over Abelian groups is investigated. Complete mappings specified by generalized feedbacκ registers and generalized Feistel networks are considered. In both cases criteria for the mapping completeness are established. A procedure for uniform sampling of quasigroups induced by complete mappings under study is suggested. The classes of quasigroups generated by generalized feedbacκ shift registers or generalized Feistel networks and by the permutation construction applied to proper families of functions are shown to be disjoint. [ABSTRACT FROM AUTHOR]

We prove a topological completeness theorem for the modal logic GLP containing operators { ⟨ ξ ⟩ : ξ ∈ Ord } intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space X, any sentence ϕ consistent with GLP can be satisfied on a polytopological space based on finitely many Icard topologies constructed over X and corresponding to the finitely many modalities that occur in ϕ . [ABSTRACT FROM AUTHOR]

The increasing significance of theorem proving-based formalization in mathematics and computer science highlights the necessity for formalizing foundational mathematical theories. In this work, we employ the Coq interactive theorem prover to methodically formalize the language, semantics, and syntax of propositional logic, a fundamental aspect of mathematical reasoning and proof construction. We construct four Hilbert-style axiom systems and a natural deduction system for propositional logic, and establish their equivalences through meticulous proofs. Moreover, we provide formal proofs for essential meta-theorems in propositional logic, including the Deduction Theorem, Soundness Theorem, Completeness Theorem, and Compactness Theorem. Importantly, we present an exhaustive formal proof of the Completeness Theorem in this paper. To bolster the proof of the Completeness Theorem, we also formalize concepts related to mappings and countability, and deliver a formal proof of the Cantor–Bernstein–Schröder theorem. Additionally, we devise automated Coq tactics explicitly designed for the propositional logic inference system delineated in this study, enabling the automatic verification of all tautologies, all internal theorems, and the majority of syntactic and semantic inferences within the system. This research contributes a versatile and reusable Coq library for propositional logic, presenting a solid foundation for numerous applications in mathematics, such as the accurate expression and verification of properties in software programs and digital circuits. This work holds particular importance in the domains of mathematical formalization, verification of software and hardware security, and in enhancing comprehension of the principles of logical reasoning. [ABSTRACT FROM AUTHOR]

Socio-cyber-physical systems (SCPSs) have emerged as networked heterogeneous systems that incorporate social components (e.g., business processes and social networks) along with physical (e.g., Internet-of-Things devices) and software components. Model-driven techniques for building SCPSs need actor and goal models to capture social concerns, whereas system issues are often addressed with the Systems Modeling Language (SysML). Comprehensive traceability between these types of models is essential to support consistency and completeness checks, change management, and impact analysis. However, traceability management between these complementary views is not well supported across SysML tools, particularly when models evolve because SysML does not provide sophisticated out-of-the-box goal modeling capabilities. In our previous work, we proposed a model-based framework, called CGS4Adaptation, that supports basic traceability by importing goal and SysML models into a leading third-party requirement-management system, namely IBM Rational DOORS. In this paper, we present the framework's traceability management method and its use for automated consistency and completeness checks. Traceability management also includes implicit link detection, thereby, improving the quality of traceability links while better aligning designs with requirements. The method is evaluated using an adaptive SCPS case study involving an IoT-based smart home. The results suggest that the tool-supported method is effective and useful in supporting the traceability management process involving complex goal and SysML models in one environment while saving development time and effort. [ABSTRACT FROM AUTHOR]

We study arbitrary intermediate propositional logics extended with a collection of axioms from (classical) justification logics. For these, we introduce various semantics by combining either Heyting algebras or Kripke frames with the usual semantic machinery used by Mkrtychev's, Fitting's or Lehmann and Studer's models for classical justification logics. We prove unified completeness theorems for all intermediate justification logics and their corresponding semantics using a respective propositional completeness theorem of the underlying intermediate logic. Further, by a modification of a method of Fitting, we prove unified realization theorems for a large class of intermediate justification logics and accompanying intermediate modal logics. [ABSTRACT FROM AUTHOR]

We introduce a logic for a class of probabilistic Kripke structures that we call type structures, as they are inspired by Harsanyi type spaces. The latter structures are used in theoretical economics and game theory. A strong completeness theorem for an associated infinitary propositional logic with probabilistic operators was proved by Meier. By simplifying Meier's proof, we prove that our logic is strongly complete with respect to the class of type structures. In order to do that, we define a canonical model (in the sense of modal logics), which turns out to be a terminal object in a suitable category. Furthermore, we extend some standard model-theoretic constructions to type structures and we prove analogues of first-order results for those constructions. [ABSTRACT FROM AUTHOR]

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We obtain several variants of the classic von Neumann–Morgenstern expected utility theorem with and without the completeness axiom in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary separable metric space, and the utility functions are allowed to be unbounded. The main ingredient of our results is a novel (behavioral) axiom on the underlying preference relations, which is satisfied by virtually all stochastic orders. The proof of the main representation theorem is built on the fact that the dual of the Kantorovich–Rubinstein space is (isometrically isomorphic to) the Banach space of Lipschitz functions that vanish at a fixed point. An application to the theory of nonexpected utility is also provided. [ABSTRACT FROM AUTHOR]

On L - fuzzy normed spaces, which is the generalization of fuzzy spaces, the notion of lacunary statistical convergence for double sequences which is a generalization of statistical convergence, are studied and developed in this paper. In addition, the definitions of lacunary statistical Cauchy and completeness for double sequences and related theorems are given on L - fuzzy normed spaces. Also, the relationship of lacunary statistical Cauchyness and lacunary statistical boundedness for double sequences with respect to L - fuzzy norm is shown. [ABSTRACT FROM AUTHOR]

Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized by optimization techniques and, increasingly, by machine-learning methods. We study this approach from a programming-language perspective. We define two small languages that support decision-making abstractions: one with choices and rewards, and the other additionally with probabilities. We give both operational and denotational semantics. In the case of the second language we consider three denotational semantics, with varying degrees of correlation between possible program values and expected rewards. The operational semantics combine the usual semantics of standard constructs with optimization over spaces of possible execution strategies. The denotational semantics, which are compositional, rely on the selection monad, to handle choice, augmented with an auxiliary monad to handle other effects, such as rewards or probability. We establish adequacy theorems that the two semantics coincide in all cases. We also prove full abstraction at base types, with varying notions of observation in the probabilistic case corresponding to the various degrees of correlation. We present axioms for choice combined with rewards and probability, establishing completeness at base types for the case of rewards without probability. [ABSTRACT FROM AUTHOR]

Our aim is to introduce the concept of double-measure ergodic and double-measure pseudo-almost periodic functions in Stepanov's sense. In addition, we present numerous interesting results, such as the composition theorems and completeness properties, for these two spaces of considered functions. We also establish the existence and uniqueness for double-measure pseudo-almost periodic mild solutions in Stepanov's sense for some evolution equations. [ABSTRACT FROM AUTHOR]

We study the lattice of extensions of four-valued Belnap–Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and prove some new completeness theorems for super-Belnap logics. The crucial technical tool for this purpose will be the so-called antiaxiomatic (or explosive) part operator. The antiaxiomatic (or explosive) extensions of Belnap–Dunn logic turn out to be of particular interest owing to their connection to graph theory: the lattice of finitary antiaxiomatic extensions of Belnap–Dunn logic is isomorphic to the lattice of upsets in the homomorphism order on finite graphs (with loops allowed). In particular, there is a continuum of finitary super-Belnap logics. Moreover, a non-finitary super-Belnap logic can be constructed with the help of this isomorphism. As algebraic corollaries we obtain the existence of a continuum of antivarieties of De Morgan algebras and the existence of a prevariety of De Morgan algebras which is not a quasivariety. [ABSTRACT FROM AUTHOR]

In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm | ⋅ | 한 and we discuss some topological and geometric concepts such as completeness, convexity, strict convexity and uniform convexity in the bicomplex setting with respect to the hyperbolic-valued norm ∥ ⋅ ∥ 픻 , ⋅ by defining the concept of 픻 -normed Banach bicomplex A-module and constructing 픻 -normed Banach bicomplex 픹 ⁢ ℂ -modules l p 한 ⁢ (픹 ⁢ ℂ) . [ABSTRACT FROM AUTHOR]

We construct a 2-equivalence CohTheory op ≃ TypeSpaceFunc . Here CohTheory is the 2-category of positive theories and TypeSpaceFunc is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in CohTheory . The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is 'the same' as the collection of its type spaces (i.e. its type space functor). In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory. The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories. [ABSTRACT FROM AUTHOR]