Search results for "COMPLETENESS"
showing 6 items of 66 documents
What is Mathematics: Gödel's Theorem and Around (Edition 2013)
2013
Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2013. ATTENTION! New Edition 2015 available at https://dspace.lu.lv/dspace/handle/7/5306.
Modal Consequence Relations Extending S4.3: An Application of Projective Unification
2016
We characterize all finitary consequence relations over $\mathbf{S4.3}$ , both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic $L$ extending $\mathbf{S4}$ has projective unification if and only if $L$ contains $\mathbf{S4.3}$ . In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relation…
Introduction to Mathematical Logic, Edition 2021
2021
Textbook for students in mathematical logic. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux and resolution methods. Herbrand's theorem. Sections 1, 2, 3 represent an extended translation of the corresponding chapters of the book: V. Detlovs, Elements of Mathematical Logic, Riga, University of Latvia, 1964, 252 pp. (in Latvian).
Predictive models in assessment of macroinvertebrates in boreal rivers
2009
Jukka Aroviita tutki väitöskirjassaan jokien ja purojen biologisen tilan mittaamismenetelmiä. Aroviita osoitti, että ihmistoiminnan aiheuttamat biologiset muutokset voivat jäädä havaitsematta, jos eliöyhteisöjen luonnollista taustavaihtelua ei oteta kunnolla huomioon.- Tällöin vesistöjen saatetaan arvioida olevan paremmassa kunnossa kuin ne todellisuudessa ovatkaan. Muutosten tunnistamistarkkuuden tulisi olla mahdollisimman hyvä, sillä tila-arvioilla on myös juridisesti määräytyviä yhteiskunnallisia ja taloudellisia seuraamuksia, Aroviita toteaa. Vielä 1990-luvulla järvien ja jokien tilaa arvioitiin suurelta osin ihmisen näkökulmasta ja veden kemian perusteella. Nykylainsäädäntö edellyttää …
Sensitivity of bipartite network analyses to incomplete sampling and taxonomic uncertainty
2023
Bipartite network analysis is a powerful tool to study the processes structuring interactions in ecological communities. In applying the method, it is assumed that the sampled interactions provide an accurate representation of the actual community. However, acquiring a representative sample may be difficult as not all species are equally abundant or easily identifiable. Two potential sampling issues can compromise the conclusions of bipartite network analyses: failure to capture the full range of interactions (sampling completeness) and use of a taxonomic level higher than species to evaluate the network (taxonomic resolution). We asked how commonly used descriptors of bipartite antagonisti…
A Completeness Proof for a Regular Predicate Logic with Undefined Truth Value
2023
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of "is defined" is extended to terms and formulas via a straightforward recursive algorithm. The "is defined" formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the formula, its negation, and the negation of its "is defined" formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions …