The study of biodiversity spans many disciplines and includes data pertaining to species distributions and abundances, genetic sequences, trait measurements, and ecological niches, complemented by information on collection and measurement protocols. A review of the current landscape of metadata standards and ontologies in biodiversity science suggests that existing standards such as the Darwin Core terminology are inadequate for describing biodiversity data in a semantically meaningful and computationally useful way. Existing ontologies, such as the Gene Ontology and others in the Open (...) Biological and Biomedical Ontologies (OBO) Foundry library, provide a semantic structure but lack many of the necessary terms to describe biodiversity data in all its dimensions. In this paper, we describe the motivation for and ongoing development of a new Biological Collections Ontology, the Environment Ontology, and the Population and Community Ontology. These ontologies share the aim of improving data aggregation and integration across the biodiversity domain and can be used to describe physical samples and sampling processes (for example, collection, extraction, and preservation techniques), as well as biodiversity observations that involve no physical sampling. Together they encompass studies of: 1) individual organisms, including voucher specimens from ecological studies and museum specimens, 2) bulk or environmental samples (e.g., gut contents, soil, water) that include DNA, other molecules, and potentially many organisms, especially microbes, and 3) survey-based ecological observations. We discuss how these ontologies can be applied to biodiversity use cases that span genetic, organismal, and ecosystem levels of organization. We argue that if adopted as a standard and rigorously applied and enriched by the biodiversity community, these ontologies would significantly reduce barriers to data discovery, integration, and exchange among biodiversity resources and researchers. (shrink)

We present a case study of grammatical constructions and how their function in a single language can be captured through semantic and syntactic classification. Since 2016 an on-going joint project of UiT The Arctic University of Norway and the National Research University Higher School of Economics in Moscow has been collecting and analyzing multiword grammatical constructions of Russian. The main product is the Russian Constructicon, which, with over two thousand two hundred constructions, is arguably the largest openly available constructicon resource (...) for any language. The combination of this large size with depth of analysis, containing both syntactic and semantic tags, makes it possible to view the interrelation of constructions as families and to discover trends in their behavior. Our annotation includes 53 semantic tags of varying frequency, with three tags that are by far more frequent than all the rest, accounting for 30% of the entire inventory of the Russian Constructicon. These three semantic types are Assessment, Attitude, and Intensity, all of which convey a speaker’s evaluation of a topic, in contrast to most of the other tags. Assessment and Attitude constructions are investigated in greater detail in this article. Secondary semantic tags reveal that negative evaluation among these two semantic types is more than twice as frequent as positive evaluation. Examples of negative evaluations are: for Assessment VP tak sebe, as in Na pianino ja igraju tak sebe “I play the piano so-so [lit. thus self]”; for Attitude s PronPers-Gen xvatit/xvatilo, as in S menja xvatit “I’m fed up [lit. from me enough].” In terms of syntax, the most frequent syntactic types of constructions in the Russian Constructicon are clausal constructions [constituting an independent clause like s PronPers-Gen xvatit/xvatilo ] and constructions with the anchor in the role of adverbial modifier. Our semantic and syntactic classification of this large body of Russian constructions makes it possible to postulate patterns of grammatical constructions constituting a radial category with central and peripheral types. Classification of large numbers of constructions reveals systematic relations that structure the grammar of a language. (shrink)

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

Dag Prawitz The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 119-122, March 2013.

It has been common in contemporary logic and philosophy of logic to identify the validity of an inference with its conclusion being a (logical) consequence of its premisses.

By a valid inference is here understood an inference that succeeds in its aim to justify its conclusion given that its premisses are already justified. For an inference to be valid it is thus not enough that the sentence asserted in the conclusion is a logical consequence of the sentences asserted in the premisses. A proof is understood as a succession of valid inferences that is closed (i.e. all its assumptions are discharged and all its free variables are bound by (...) some of the inferences). On the other hand, in mathematics the justification of an assertion has traditionally been taken to consist in a proof of it, which gives rise to an explanatory circle.In an attempt to avoid this circle, I have in previous works tried to explain the notion of ground for an assertion without referring to valid inferences. However, it turns out that the resulting notion of ground has unwanted consequences like the notion of proof in the so-called BHK-interpretation of intuitionistic logic. For instance, one is guaranteed a ground or a proof of an implication A → B as soon as there is in fact no ground or proof of A, regardless of whether one really knows this fact, and hence without having a real justification of the assertion of the implication.In the absence of a non-circular explanation of the notions of valid inference and proof, I suggest that we should try to formulate a number of principles of how these two epistemic notions depend on each other. A more careful explanation of the validity of an inference results in what I call a heuristic idea about the validity of inference, which is used as a guide to formulate precise principles. One such principle generalizes Gentzen’s idea that his introduction rules define the meaning of the logical constants. Another principle generalizes a previously noted property of Gentzen’s elimination rules that I have called that of satisfying the inversion principle. It results in a notion that I call non-creativity, which implies validity. (shrink)

Compositionality is a principle used in logic, philosophy, mathematics, linguistics, and computer science for assigning meanings to language expressions in a systematic manner following syntactic construction, thereby allowing for a perspicuous algebraic view of the syntax-semantics interface. Yet the status of the principle remains under debate, with positions ranging from compositionality always being achievable to its having genuine empirical content. This paper attempts to sort out some major issues in all this from a logical perspective. First, we stress the fundamental (...) harmony between Compositionality and its apparent antipode of Contextuality that locates meaning in interaction with other linguistic expressions and in other settings than the actual one. Next, we discuss basic further desiderata in designing and adjudicating a compositional semantics for a given language in harmony with relevant contextual syntactic and semantic cues. In particular, in a series of concrete examples in the realm of logic, we point out the dangers of over-interpreting compositional solutions, the ubiquitous entanglement of assigning meanings and the key task of explaining given target inferences, and the dynamics of new language design, illustrating how even established compositional semantics can be rethought in a fruitful manner. Finally, we discuss some fresh perspectives from the realm of game semantics for natural and formal languages, the general setting for Samson Abramsky’s influential work on programming languages and process logics. We highlight outside-in coalgebraic perspectives on meanings as finite or infinitely unfolding behavior that might challenge and enrich current discussions of compositionality. (shrink)

In a mathematical perspective, neighborhood models for modal logic are generalized quantifiers, parametrized to points in the domain of objects/worlds. We explore this analogy further, connecting generalized quantifier theory and modal neighborhood logic. In particular, we find interesting analogies between conservativity for linguistic quantifiers and the locality of modal logic, and between the role of invariances in both fields. Moreover, we present some new completeness results for modal neighborhood logics of linguistically motivated classes of generalized quantifiers, and raise new types (...) of open problem. With the bridges established here, many further analogies might be explored between the two fields to mutual benefit. (shrink)

An inference can be seen as a speech act, in which one passes from a number of assertions called premisses to another assertion, the conclusion, which is presented as supported or justified by the premisses. To justify the assertion that appears as conclusion is the characteristic aim of an inference. Here, we confine ourselves to deductive inferences where the justification is taken to be conclusive. A short, natural explanation of what it is for a (deductive) inference to be valid is (...) to say that it is valid if it succeeds in its aim, that is, if its premisses do (conclusively) justify the conclusion, given that premisses are justified. The paper is concerned with developing this explanation further. (shrink)

WeingartnerPaul and LeebHans-Peter, eds, Kreisel’s Interests: On the Foundations of Logic and Mathematics. Tributes; 41. London: College Publications, 2020. Pp. viii + 171. ISBN: 978-1-84890-330-2.

It is not unreasonable to think that the dispute between classical and intuitionistic mathematics might be unresolvable or 'faultless', in the sense of there being no objective way to settle it. If so, we would have a pretty case of relativism. In this note I argue, however, that there is in fact not even disagreement in any interesting sense, let alone a faultless one, in spite of appearances and claims to the contrary. A position I call classical pluralism is sketched, (...) intended to provide a coherent methodological stance towards the issue. Some reasons to recommend this stance are given, as well as some speculations as to why not everyone might want to follow the recommendation. (shrink)

According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...) this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence. (shrink)

Bu makale genel olarak karşılaştırmalı teoloji alanını Türkçe okuyucuya tanıtmayı amaçlamaktadır. Karşılaştırmalı teoloji, son yıllarda Batıda yeniden yorumlanmış ve ötekinden öğrenme düsturuyla yola çıkan akademik bir disiplin alanıdır. Bu makale karşılaştırmalı teolojiyi tanıtmakla beraber Hristiyan teolojisi içindeki yerini de sorgulayacaktır. Bu bağlamda, karşılaştırmalı teolojinin dinler teolojisine bir alternatif olup olmadığı, karşılaştırmalı teolojinin dinler teolojisinden bağımsız bir alan olarak değerlendirilip değerlendirilemeyeceği, dinler teolojisi içerisinde bir tipoloji olarak görülüp görülmediği gibi sorunlara da cevap arayacaktır. Nihayetinde bu makalede karşılaştırmalı teolojinin dinler teolojisine alternatif (...) olarak görülemeyeceği, aynı zamanda dinler teolojisi içerisinde üç veya dört yönlü tipolojilerden biri olarak da değerlendirilemeyeceği sonucuna varılmıştır. Sonuçta karşılaştırmalı teoloji ve dinler teolojisinin birbirinden bağımsız ama birbirlerini tamamlayan iki alan olduğu iddia edilecektir. (shrink)

We show how Kreisel's representation theorem for sets in the analytical hierarchy can be generalized to sets defined by positive induction and use this to estimate the complexity of constructions in the theory of domains with totality.

Reviewed Works:Gaisi Takeuti, Proof Theory.Georg Kreisel, Proof Theory: Some Personal Recollections.Wolfram Pohlers, Contributions of the Schutte School in Munich to Proof Theory.Stephen G. Simpson, Subsystems of $\mathbf{Z}_2$ and Reverse Mathematics.Solomon Feferman, Proof Theory: A Personal Report.