Search

This paper introduces two languages and associated logics designed to afford perspicuous representations of a range of natural language arguments involving adverbs and the like: first-order logic with basic adverbs (FOL-BA) and first-order logic with scoped adverbs (FOL-SA). The guiding logical idea is that an adverb can come between a term and the rest of the statement it is a part of, resulting in a logically stronger statement. I explain various interesting challenges that arise in the attempt to implement the guiding idea, and provide solutions for some but not all of them. I conclude by outlining some directions for further research. [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]

Steinsvold (2020) has provided two semantics for the basic modal language enriched with propositional quantifiers (∀p). We define an extension EM of the system KD45... and prove that EM is sound and com- plete for both semantics. It follows that the two semantics are equivalent. [ABSTRACT FROM AUTHOR]

The article is a book review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Trueman's book is a response to Willard Van Orman Quine's argument against higher-order logic. Trueman argues that terms like "to be" and "to exist" are ambiguous, and there are different concepts of existence. He defends higher-order logic and explores the way properties exist. The reviewer finds Trueman's theory to be untenable and suggests an alternative approach based on ancient Greek philosophy. The reviewer also argues that Trueman's theory does not effectively address Quine's objections to higher-order logic. [Extracted from the article]

Vardanyan's Theorems [36, 37] state that $\mathsf {QPL}(\mathsf {PA})$ —the quantified provability logic of Peano Arithmetic—is $\Pi ^0_2$ complete, and in particular that this already holds when the language is restricted to a single unary predicate. Moreover, Visser and de Jonge [38] generalized this result to conclude that it is impossible to computably axiomatize the quantified provability logic of a wide class of theories. However, the proof of this fact cannot be performed in a strictly positive signature. The system $\mathsf {QRC_1}$ was previously introduced by the authors [1] as a candidate first-order provability logic. Here we generalize the previously available Kripke soundness and completeness proofs, obtaining constant domain completeness. Then we show that $\mathsf {QRC_1}$ is indeed complete with respect to arithmetical semantics. This is achieved via a Solovay-type construction applied to constant domain Kripke models. As corollaries, we see that $\mathsf {QRC_1}$ is the strictly positive fragment of $\mathsf {QGL}$ and a fragment of $\mathsf {QPL}(\mathsf {PA})$. [ABSTRACT FROM AUTHOR]

Formalizations in first-order logic are standardly used to represent logical forms of sentences and to show the validity of ordinary-language arguments. Since every sentence admits of a variety of formalizations, a challenge arises: why should one valid formalization suffice to show validity even if there are other, invalid, formalizations? This paper suggests an explanation with reference to criteria of adequacy which ensure that formalizations are related in a hierarchy of more or less specific formalizations. This proposal is then compared with stronger criteria and assumptions, especially the idea that sentences essentially have just one logical form. [ABSTRACT FROM AUTHOR]

This paper reflects on the limits of logical form set by a novel criterion of logicality proposed in (Bonnay and Speitel, 2021). The interest stems from the fact that the delineation of logical terms according to the criterion exceeds the boundaries of standard first-order logic. Among ‘novel’ logical terms is the quantifier “there are infinitely many”. Since the structure of the natural numbers is categorically characterisable in a language including this quantifier we ask: does this imply that arithmetical forms have been reduced to logical forms? And, in general, what other conditions need to be satisfied for a form to qualify as “fully logical”? We survey answers to these questions. [ABSTRACT FROM AUTHOR]

This paper concerns an expansion of first-order Belnap-Dunn logic, called BD⊥⊃,F, and an application of this logic in the area of relational database theory. The notion of a relational database, the notion of a query applicable to a relational database, and several notions of an answer to a query with respect to a relational database are considered from the perspective of this logic, taking into account that a database may be an inconsistent database and/or a database with null values. The chosen perspective enables among other things the definition of a notion of a consistent answer to a query with respect to a possibly inconsistent database without resort to database repairs. For each of the notions of an answer considered, being an answer to a query with respect to a database of the kind considered is decidable. [ABSTRACT FROM AUTHOR]

We consider first-order infinite-valued Łukasiewicz logic and its expansion, first-order rational Pavelka logic RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other and with Hájek’s Hilbert-type calculi for the same logics. To facilitate comparing previously known calculi for the logics, we define two new analytic calculi for RPL∀ and include them in our comparison. The key part of the comparison is a density elimination proof that introduces no cuts for one of the hypersequent calculi considered. [ABSTRACT FROM AUTHOR]

Paraconsistent extensions of 3-valued Gödel logic are studied as tools for knowledge representation and nonmonotonic reasoning. Particularly, Osorio and his collaborators showed that some of these logics can be used to express interesting nonmonotonic semantics. CG'3 is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG'3 by means of Fidel structures, named CG'3-structures. These structures are constructed from enriched Boolean algebras with a special family of sets. Moreover, we also show that the most basic CG'3-structures coincide with da Costa-Alves' bi-valuation semantics; this connection is displayed through a Representation Theorem for CG'3-structures. By contrast, we show that for other paraconsistent logics that allow us to present semantics through Fidel structures, this connection is not held. Finally, Fidel semantics for the first-order version of the logic of CG'3 are presented by means of adapting algebraic tools. [ABSTRACT FROM AUTHOR]

Having effective learning and retrieval phases of satisfiability logic in Discrete Hopfield Neural Network models ensures optimal synaptic weight management, which consequently leads to the production of optimal final neuron states. However, the problem with this model is that different initial states can affect the biasedness of the retrieval phase since the model memorizes final states without generating new ones and produces suboptimal final neuron states. To date, there is no recent research that solves this issue by improving both phases in the Discrete Hopfield Neural Network that involves first-order satisfiability logic. Therefore, this research contributes to the improvement of the learning and retrieval phases by integrating the Hybrid Differential Evolution Algorithm and Swarm Mutation respectively. This research utilizes Y-Type Random 2 Satisfiability, which combines first and second-order clauses to expand the storage capacity of DHNN models, facilitating the retrieval of optimal final neuron states. To evaluate the effectiveness of the Hybrid Differential Evolution Algorithm and Swarm Mutation in the learning and retrieval phases, several performance metrics are employed in terms of synaptic weight management, learning errors, testing errors, energy profiles, solution variations, and similarity for 10 different cases. Quantitative evaluations show that the proposed model successfully enhances the optimization of both phases, ranking first compared to 10 recent algorithms for all metrics. In terms of convergence analysis, the proposed model progressed fast towards the optimal solution with only one iteration for all cases. Additionally, the proposed model can generate a 100 % global minima ratio when dealing with a high number of neurons for Case 5. • A novel logical rule as output symbols of DHNN was proposed. • HDEA was utilized to optimize the learning phase of DHNN. • A mutation-based retrieval phase of DHNN was proposed. • The results showed that the proposed model outperformed other baseline models. [ABSTRACT FROM AUTHOR]

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences (consequences for which epistemic closure certainly holds) from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], an expressive fragment of classical game semantics that weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of some first-order sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is needed to obtain a better solution of the problem. In this paper, I argue that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be formulated as follows: when inquiring after the truth-value of ∀xφ, an individual might be unaware of all substitutional instances this sentence accepts, but at least she must know that, if an element a is given, then ∀xφ holds only if φ(x/a) is true. This thesis accepts game-theoretic formaliza- tion in terms of a refinement of urn semantics. I maintain that the system so obtained (US+) affords an improved solution of the logical omniscience problem. To do this, I characterize first-order theoremhood in US+. As a consequence of this result, we will see that the ideal reasoner depicted by US+ only knows the validity of first-order formulas whose Herbrand witnesses can be trivially found, a fact that provides strong evidence that our refinement of urn semantics captures a relevant sense of logical obviousness. [ABSTRACT FROM AUTHOR]

This paper considers the applicative computing technology (ACT), within the framework of which the semantic analysis of a number of natural language constructs is performed. The necessary elements of grammatical analysis are involved. Much first-order logical means is used, and predicate variables are necessarily used for analysis. At the same time, the advantages of higher-order systems, which include ACT, are extracted. The fact is that the semantics of a natural language is characterized by a multi-tiered nesting of grammatical structures, which conflicts with first-order logical systems. [ABSTRACT FROM AUTHOR]

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not. [ABSTRACT FROM AUTHOR]

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. 'Whitehead and Russell wrote Principia Mathematica'), while in others they are not (e.g. 'Some philosophers wrote Principia Mathematica'). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called 'discrete plural logic') is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic--or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. [ABSTRACT FROM AUTHOR]

We will formulate some analogous higher-order versions of Skolem's paradox and assess the generalizability of two solutions for Skolem's paradox to these paradoxes: the textbook approach and that of Bays (2000). We argue that the textbook approach to handle Skolem's paradox cannot be generalized to solve the parallel higher-order paradoxes, unless it is augmented by the claim that there is no unique language within which the practice of mathematics can be formalized. Then, we argue that Bays' solution to the original Skolem's paradox, unlike the textbook solution, can be generalized to solve the higher-order paradoxes without any implication about the possibility or order of a language in which mathematical practice is to be formalized. [ABSTRACT FROM AUTHOR]

This paper is a first-order interdisciplinary research, in an interstice defined by linguistic statistics and it appeared by extending the statistical way of thinking in the universe of language. The research structure includes an introductory section that states the specific paradigm or the common statistical and linguistic concepts of the investigation, followed by a brief methodological section, simultaneously of a descriptive and applied type, with reference to laws, methods and statistical models possible in the initially quantitative universe and finally qualitative universe of language, to eventually reach the final section dedicated to an attempt to assess entropy and information energy, based on the results of research in its whole. From an evolutionary point of view, after the philologist initially investigates in an exemplary way and with philological accuracy, and the statistician approaches selectively and inferentially, but also with specific statistical rigor, the interdisciplinary point of view of linguistic statistics allows a rapid confrontation and a multiple evaluation of entropy through the information energy method, but also through other equally interesting methods. The justified hope of interdisciplinary thinking of linguistic statistics to optimally capitalize on simultaneously philological and methodological reasoning to validate or invalidate preliminary hypotheses and to allow the expression of conclusions, follow-up analysis, outlines if not an answer, certainly at least several useful questions, which confirms practically and theoretically both the necessity and the veracity of the research in this article, according to the logic of a successful research in a Veblenian way. [ABSTRACT FROM AUTHOR]

This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite. [ABSTRACT FROM AUTHOR]

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. [ABSTRACT FROM AUTHOR]

We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of varying strength. For all presented calculi a constructive cut elimination is provided. [ABSTRACT FROM AUTHOR]

We introduce the framework of AECats (abstract elementary categories), generalizing both the category of models of some first-order theory and the category of subsets of models. Any AEC and any compact abstract theory ("cat", as introduced by Ben-Yaacov) forms an AECat. In particular, we find applications in positive logic and continuous logic: the category of (subsets of) models of a positive or continuous theory is an AECat. The Kim–Pillay theorem for first-order logic characterizes simple theories by the properties dividing independence has. We prove a version of the Kim–Pillay theorem for AECats with the amalgamation property, generalizing the first-order version and existing versions for positive logic. [ABSTRACT FROM AUTHOR]

Copyright of Discurso is the property of Universidade Aberta and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Self-knowledge (SK) is a natural ability of the human cognitive system and is defined as a complex re-representation of knowledge subject has about her own internal states. It is composed of two basic representations: the representation of I and the representation of the experienced state. SK has a propositional (i.e. language-like) form and can be expressed in the form of self-reports like "I believe that I believe that p". It has then the form of a second-order belief which, as a re-representation, generates the following problem concerning false representations: if the first-order representations of the I or of experienced states can be false like in cases of self-illusions or disorders like somatoparaphrenia, then how can error in self-cognition inherited by the re-representation (i.e. by SK) be avoided? I claim that the re-representational model of SK is a useful but artificial tool for the description of the components of SK; however, it is misleading to think of it as capturing the truth about SK. I propose here a representational model of SK which reduces those beliefs constituting SK to first-order beliefs which are sufficient as constituents of SK. [ABSTRACT FROM AUTHOR]

In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove sev- eral important meta-theorems. The calculus, denoted as CB¹, is an exten- sion of systems PI, Cmin and B¹, and a proper subsystem of Sette's calculus P1. We also investigate the generalization of CB1 to the hierarchy of related calculi. [ABSTRACT FROM AUTHOR]

We present a study of unpublished fragments of Jan F. Drewnowski's manuscript from the years 1922-1928, which contains his own axiomatics for mereology. The sources are transcribed and two versions of mereology are reconstructed from them. The first one is given by Drewnowski. The second comes from Lesniewski and was known to Drewnowski from Lesniewski's lectures. Drewnowski's version is expressed in the language of ontology enriched with the primitive concept of a (proper) part, and its key axiom expresses the so-called weak super-supplementation principle, which was named by Drewnowski "the postulate of the existence of subtractions". Lesniewski's axiomatics with the primitive concept of an ingrediens contains the axiom expressing the strong super-supplementation principle. In both systems the collective class of objects from the range of a given non-empty concept is defined as the upper bound of that range. From a historical point of view it is interesting to notice that the presented version of Lesniewski's axiomatics has not been published yet. The same applies to Drewnowski's approach. We reconstruct the proof of the equivalence of these two systems. Finally, we discuss questions stemming from their equivalence in frame of elementary mereology formulated in a modern way. [ABSTRACT FROM AUTHOR]

Process modeling has a broad range of applications, varying from business and system engineering, via artifact design, up to natural process modeling utilized in natural sciences. Over the last decades, various sophisticated languages and frameworks have been developed to support process modeling. The current paper discusses an approach to process modeling, which is, in contrast to many existing solutions, intended for the integrated process and object modeling. Furthermore, it is designed to be a lightweight approach with only a few constructs, which, however, permit the representation of processes from various perspectives. The developed solution provides an abstract language-independent model (ontology), partial formalization in first-order logic as well as a Web Ontology Language (OWL) implementation. [ABSTRACT FROM AUTHOR]

We study the fluted fragment, a decidable fragment of first-order logic with an unbounded number of variables, motivated by the work of W. V. Quine. We show that the satisfiability problem for this fragment has nonelementary complexity, thus refuting an earlier published claim by W. C. Purdy that it is in NExpTime. More precisely, we consider ${\cal F}{{\cal L}^m}$ , the intersection of the fluted fragment and the m -variable fragment of first-order logic, for all $m \ge 1$. We show that, for $m \ge 2$ , this subfragment forces $\left\lfloor {m/2} \right\rfloor$ -tuply exponentially large models, and that its satisfiability problem is $\left\lfloor {m/2} \right\rfloor$ - NExpTime -hard. We further establish that, for $m \ge 3$ , any satisfiable ${\cal F}{{\cal L}^m}$ -formula has a model of at most ( $m - 2$)-tuply exponential size, whence the satisfiability (= finite satisfiability) problem for this fragment is in ( $m - 2$)- NExpTime. Together with other, known, complexity results, this provides tight complexity bounds for ${\cal F}{{\cal L}^m}$ for all $m \le 4$. [ABSTRACT FROM AUTHOR]

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First-Order Logic is equivalent to some first-order sentence. In this work it is shown that all nontrivial dependency atoms that are strongly first order, downwards closed, and relativizable (in the sense that the relativizations of the corresponding atoms with respect to some unary predicate are expressible in terms of them) are definable in terms of constancy atoms. Additionally, it is shown that any strongly first-order dependency is safe for any family of downwards closed dependencies, in the sense that every sentence of the logic obtained by adding to First-Order Logic both the strongly first-order dependency and the downwards closed dependencies is equivalent to some sentence of the logic obtained by adding only the downwards closed dependencies. [ABSTRACT FROM AUTHOR]

In this paper, a visual domain ontology (VDO) is constructed using OWL-Lite Language. The VDO passes through two execution phases, namely, construction and inferring phases. In the construction phase, OWL classes are initialized, with reference to annotated scenes, and connected by hierarchical, spatial, and content-based relationships (presence/absence of some objects depends on other objects). In the inferring phase, the VDO is used to infer knowledge about an unknown scene. This paper aims to use a standard language, namely, OWL, to represent non-standard visual knowledge; facilitate straightforward ontology enrichment; and define the rules for inferring based on the constructed ontology. The OWL standardizes the constructed knowledge and facilitates advanced inferring because it is built on top of the first-order logic and description logic. The VDO then allows an efficient representation and reasoning of complex visual knowledge. In addition to representation, the VDO enables easy extension, sharing, and reuse of the represented visual knowledge. [ABSTRACT FROM AUTHOR]

AGM contraction and revision assume an underlying logic that contains propositional logic. Consequently, this assumption excludes many useful logics such as the Horn fragment of propositional logic and most description logics. Our goal in this paper is to generalise AGM contraction and revision to (near-)arbitrary fragments of classical first-order logic. To this end, we first define a very general logic that captures these fragments. In so doing, we make the modest assumptions that a logic contains conjunction and that information is expressed by closed formulas or sentences. The resulting logic is called first-order conjunctive logic or FC logic for short. We then take as the point of departure the AGM approach of constructing contraction functions through epistemic entrenchment, that is the entrenchment-based contraction. We redefine entrenchment-based contraction in ways that apply to any FC logic, which we call FC contraction. We prove a representation theorem showing its compliance with all the AGM contraction postulates except for the controversial recovery postulate. We also give methods for constructing revision functions through epistemic entrenchment which we call FC revision; which also apply to any FC logic. We show that if the underlying FC logic contains tautologies then FC revision complies with all the AGM revision postulates. Finally, in the context of FC logic, we provide three methods for generating revision functions via a variant of the Levi Identity, which we call contraction, withdrawal and cut generated revision, and explore the notion of revision equivalence. We show that withdrawal and cut generated revision coincide with FC revision and so does contraction generated revision under a finiteness condition. [ABSTRACT FROM AUTHOR]

Givant [6] generalized the notion of an atomic pair-dense relation algebra from Maddux [13] by defining the notion of a measurable relation algebra , that is to say, a relation algebra in which the identity element is a sum of atoms that can be measured in the sense that the "size" of each such atom can be defined in an intuitive and reasonable way (within the framework of the first-order theory of relation algebras). In Andréka--Givant [2], a large class of examples of such algebras is constructed from systems of groups, coordinated systems of isomorphisms between quotients of the groups, and systems of cosets that are used to "shift" the operation of relative multiplication. In Givant--Andréka [8], it is shown that the class of these full coset relation algebras is adequate to the task of describing all measurable relation algebras in the sense that every atomic and complete measurable relation algebra is isomorphic to a full coset relation algebra. Call an algebra $\mathfrak{A}$ a coset relation algebra if $\mathfrak{A}$ is embeddable into some full coset relation algebra. In the present article, it is shown that the class of coset relation algebras is equationally axiomatizable (that is to say, it is a variety), but that no finite set of sentences suffices to axiomatize the class (that is to say, the class is not finitely axiomatizable). [ABSTRACT FROM AUTHOR]

The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics. [ABSTRACT FROM AUTHOR]

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains with infinite residue fields in terms of a suitable generalization of the prime radical relation. For Bézout domains these conditions are also necessary. [ABSTRACT FROM AUTHOR]

We study universal minimal flows of the homeomorphism groups of generalized Ważewski dendrites W P , $P \subseteq \left\{ {3,4, \ldots ,\omega } \right\}$. If P is finite, we prove that the universal minimal flow of the homeomorphism group H (W P ) is metrizable and we compute it explicitly. This answers a question of Duchesne. If P is infinite, we show that the universal minimal flow of H (W P ) is not metrizable. This provides examples of topological groups which are Roelcke precompact and have a nonmetrizable universal minimal flow with a comeager orbit. [ABSTRACT FROM AUTHOR]

In this article, we will show that ${\rm{R}}{{\rm{T}}^2} + WK{L_0}$ is a ${\rm{\Pi }}_1^1$ -conservative extension of ${\rm{B\Sigma }}_3^0$. [ABSTRACT FROM AUTHOR]

We propose a method to combine the interpretability and expressive power of first-order logic with the effectiveness of neural network learning. In particular, we introduce a lifted framework in which first-order rules are used to describe the structure of a given problem setting. These rules are then used as a template for constructing a number of neural networks, one for each training and testing example. As the different networks corresponding to different examples share their weights, these weights can be efficiently learned using stochastic gradient descent. Our framework provides a flexible way for implementing and combining a wide variety of modelling constructs. In particular, the use of first-order logic allows for a declarative specification of latent relational structures, which can then be efficiently discovered in a given data set using neural network learning. Experiments on 78 relational learning benchmarks clearly demonstrate the effectiveness of the framework. [ABSTRACT FROM AUTHOR]

We present abstract complexity results about Coquand and Hyland–Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical process game semantics can model and apply to. In particular, we provide a novel method to bound the length of interactions between visible strategies and to measure precisely the tower of exponentials defining the worst-case complexity. Our study improves the old estimates on average by several exponentials. [ABSTRACT FROM PUBLISHER]

We use axioms of abstract ternary relations to define the notion of a free amalgamation theory. These form a subclass of first-order theories, without the strict order property, encompassing many prominent examples of countable structures in relational languages, in which the class of algebraically closed substructures is closed under free amalgamation. We show that any free amalgamation theory has elimination of hyperimaginaries and weak elimination of imaginaries. With this result, we use several families of well-known homogeneous structures to give new examples of rosy theories. We then prove that, for free amalgamation theories, simplicity coincides with NTP2 and, assuming modularity, with NSOP3 as well. We also show that any simple free amalgamation theory is 1-based. Finally, we prove a combinatorial characterization of simplicity for Fraïssé limits with free amalgamation, which provides new context for the fact that the generic Kn-free graphs are SOP3, while the higher arity generic $K_n^r$-free r-hypergraphs are simple. [ABSTRACT FROM PUBLISHER]

The modal characterization theorem by J. van Benthem characterizes classical modal logic as the bisimulation invariant fragment of first-order logic. In this paper, we prove a similar characterization theorem for intuitionistic modal logic. For this purpose we introduce the notion of modal asimulation as an analogue of bisimulations. The paper treats four different fragments of first-order logic induced by their respective versions of Kripke-style semantics for modal intuitionistic logic. It is shown further that this characterization can be easily carried over to arbitrary first-order definable subclasses of classical first-order models. [ABSTRACT FROM AUTHOR]

In this work we propose a comprehensive framework based on first-order logic (FOL) for mitigating (identifying and addressing) interactions between multiple clinical practice guidelines (CPGs) applied to a multi-morbid patient while also considering patient preferences related to the prescribed treatment. With this framework we respond to two fundamental challenges associated with clinical decision support: (1) concurrent application of multiple CPGs and (2) incorporation of patient preferences into the decision making process. We significantly expand our earlier research by (1) proposing a revised and improved mitigation-oriented representation of CPGs and secondary medical knowledge for addressing adverse interactions and incorporating patient preferences and (2) introducing a new mitigation algorithm. Specifically, actionable graphs representing CPGs allow for parallel and temporal activities (decisions and actions). Revision operators representing secondary medical knowledge support temporal interactions and complex revisions across multiple actionable graphs. The mitigation algorithm uses the actionable graphs, revision operators and available (and possibly incomplete) patient information represented in FOL. It relies on a depth-first search strategy to find a valid sequence of revisions and uses theorem proving and model finding techniques to identify applicable revision operators and to establish a management scenario for a given patient if one exists. The management scenario defines a safe (interaction-free) and preferred set of activities together with possible patient states. We illustrate the use of our framework with a clinical case study describing two patients who suffer from chronic kidney disease, hypertension, and atrial fibrillation, and who are managed according to CPGs for these diseases. While in this paper we are primarily concerned with the methodological aspects of mitigation, we also briefly discuss a high-level proof of concept implementation of the proposed framework in the form of a clinical decision support system (CDSS). The proposed mitigation CDSS "insulates" clinicians from the complexities of the FOL representations and provides semantically meaningful summaries of mitigation results. Ultimately we plan to implement the mitigation CDSS within our MET (Mobile Emergency Triage) decision support environment. [ABSTRACT FROM AUTHOR]

We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via EXPTIME and 2EXPTIME to undecidable. [ABSTRACT FROM AUTHOR]

A simple method is proposed to design parallel cascade controllers for open loop unstable processes. A proportional (P)controller is considered for the secondary loop and a proportional integral (PI) controller is considered for the primary loop (P/PI control configuration). Coefficients of the corresponding powers of s (Laplace variable), in the numerator is matched with the coefficients of the corresponding powers of s in the denominator of a closed loop transfer function for a servo problem. Three simulation case studies are considered in this paper. The first case involves a stable secondary loop process and an unstable primary process, the second case involves both unstable primary and secondary processes and the third one, a simulation application to a nonlinear bioreactor model equations. For comparison purposes, P/PI controller design is also carried out by improved simultaneous relay autotuning method, synthesis method and minimizing ISE criterion method. It is found that the proposed method gives a better performance. Robust stability analysis using the complimentary sensitivity function is carried out. The present method is found to be more robust. [ABSTRACT FROM AUTHOR]

We consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with negligibility, comparability and proximity the binary predicates N , C and P and the connectives [ N ] , [ C ] and [ P ] , we consider a first-order theory based on these predicates and a modal logic based on these connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic. [ABSTRACT FROM AUTHOR]

This paper introduces a new type of collision attack on first-order masked Advanced Encryption Standards. This attack is a known-plaintext attack, while the existing collision attacks are chosen-plaintext attacks. In addition, our method requires significantly fewer power measurements than any second-order differential power analysis or existing collision attacks. [ABSTRACT FROM AUTHOR]

This paper describes an approach to formulate queries in the language of first order logic over data from disparate sources distributed over a network. The data sources are treated as if they were all in a common database. The data sources may incorporate different stored or computed methods of providing data– web services and REST APIs, XML/JSON repositories, web pages, full featured databases, flat files, etc. We describe the technical foundations and benefits of this approach and compare it to other extant solutions to this problem. This approach enables end users to formulate ad-hoc queries in logic to correlate the data sources. For programmers creating applications, using a logic-based language to specify correlation criteria shortens the development life cycle and reduces cost of maintenance, compared to manually coding the equivalent correlation algorithms in procedural languages. [ABSTRACT FROM AUTHOR]