| 1. |
- Bennet, Christian, 1954, et al.
(författare)
-
Never trust an unsound theory
- 2022
-
Ingår i: Theoria. - : Wiley. - 0040-5825 .- 1755-2567. ; 88:5, s. 1053-1056
-
Tidskriftsartikel (refereegranskat)abstract
- Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in fact not Gödel sentences.
|
|
| 2. |
- Bernardy, Jean-Philippe, 1978, et al.
(författare)
-
A Compositional Bayesian Semantics for Natural Language
- 2018
-
Ingår i: Proceedings of the First International Workshop on Language Cognition and Computational Models, COLING 2018, August 20, 2018 Santa Fe, New Mexico, USA. - : COLING. - 1525-2477. - 9781948087575
-
Konferensbidrag (refereegranskat)abstract
- We propose a compositional Bayesian semantics that interprets declarative sentences in a natural language by assigning them probability conditions. These are conditional probabilities that estimate the likelihood that a competent speaker would endorse an assertion, given certain hypotheses. Our semantics is implemented in a functional programming language. It estimates the marginal probability of a sentence through Markov Chain Monte Carlo (MCMC) sampling of objects in vector space models satisfying specified hypotheses. We apply our semantics to examples with several predicates and generalised quantifiers, including higher-order quantifiers. It captures the vagueness of predication (both gradable and non-gradable), without positing a precise boundary for classifier application. We present a basic account of semantic learning based on our semantic system. We compare our proposal to other current theories of probabilistic semantics, and we show that it offers several important advantages over these accounts.
|
|
| 3. |
- Bernardy, Jean-Philippe, 1978, et al.
(författare)
-
A Logic with Measurable Spaces for Natural Language Semantics
- 2019
-
Ingår i: TbiLLC 2019: Thirteenth International Tbilisi Symposium on Language, Logic and Computation,16-20 September 2019..
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We present a Logic with Measurable Spaces (LMS) and argue that it is suitable to represent the semantics of many natural language phenomena. LMS draws inspiration from several sources. It is decidable (like description logics). It features Sigma spaces (like Martin-Löf type-theory). It internalises the notion of the cardinality (in fact, here, measures) of spaces and ratios thereof, allowing to capture the notion of event probability. In addition, LMS is arguably a concise system. Thanks to all these qualities, we hope that LMS can play a role in the foundations of natural language semantics.
|
|
| 4. |
- Bernardy, Jean-Philippe, 1978, et al.
(författare)
-
A logic with measurable spaces for natural language semantics
- 2020
-
Ingår i: Applied Mathematics, Informatics And Mechanics. - 1512-0074. ; 2020, s. 31-44
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We present a Logic with Measurable Spaces (LMS) and argue that it is suitable to represent the semantics of a number of natural lan- guage phenomena. LMS draws inspiration from several sources. It is decidable (like descriptive logics). It features Sigma spaces (like Martin-Lf type-theory). It internalises the notion of the cardinality (in fact, here, measures) of spaces and ratios thereof, allow- ing to capture the notion of event probability. In addition to being a powerful system, it is also concise and has a precise semantics in terms of integrals. Thanks to all these qualities, we hope that LMS can play a role in the foundations of natural language semantics.
|
|
| 5. |
- Bernardy, Jean-Philippe, 1978, et al.
(författare)
-
Bayesian Inference Semantics: A Modelling System and A Test Suite
- 2019
-
Ingår i: Proceedings of the Eighth Joint Conference on Lexical and Computational Semantics (*SEM), 6-7 June 2019, Minneapolis, Minnesota, USA / Rada Mihalcea, Ekaterina Shutova, Lun-Wei Ku, Kilian Evang, Soujanya Poria (Editors). - Stroudsburg, PA : Association for Computational Linguistics. - 9781948087933
-
Konferensbidrag (refereegranskat)abstract
- We present BIS, a Bayesian Inference Semantics, for probabilistic reasoning in natural language. The current system is based on the framework of Bernardy et al. (2018), but departs from it in important respects. BIS makes use of Bayesian learning for inferring a hypothesis from premises. This involves estimating the probability of the hypothesis, given the data supplied by the premises of an argument. It uses a syntactic parser to generate typed syntactic structures that serve as input to a model generation system. Sentences are interpreted compositionally to probabilistic programs, and the corresponding truth values are estimated using sampling methods. BIS successfully deals with various probabilistic semantic phenomena, including frequency adverbs, generalised quantifiers, generics, and vague predicates. It performs well on a number of interesting probabilistic reasoning tasks. It also sustains most classically valid inferences (instantiation, de Morgan’s laws, etc.). To test BIS we have built an experimental test suite with examples of a range of probabilistic and classical inference patterns.
|
|
| 6. |
- Bernardy, Jean-Philippe, 1978, et al.
(författare)
-
Bayesian Inference Semantics for Natural Language
- 2022
-
Ingår i: Probabilistic Approaches to Linguistic Theory / edited by Jean-Philippe Bernardy, Rasmus Blanck, Stergios Chatzikyriakidis, Shalom Lappin, Aleksandre Maskharashvili.. - Stanford : CSLI Publications. - 9781684000791 ; , s. 161-228
-
Bokkapitel (refereegranskat)abstract
- We present a Bayesian Inference Semantics for natural language, which computes the probability conditions of sentences compositionally, through semantic functions matching with the types of their syntactic constituents. This system captures the vagueness of classifier terms and scalar modifiers. It also offers a straightforward treatment of the sorites paradox. Our framework expresses probabilistic inferences, which rely on lexically encoded priors, and it captures the effect of informational update on these inferences, through Bayesian modelling. The central device with which we represent probabilistic interpretation is the assignment of measurable spaces to objects and properties. We estimate the probability of a predication by measuring the density of relevant objects in the space of the property that the predicate denotes. We explore two alternative models for the priors. The first one is based on Gaussian distributions, but it exhibits computational intractability with some cases of Monte Carlo sampling. The second is based on uniform densities, and in a number of important instances, it allows us to avoid Monte Carlo sampling. We construct a test suite to illustrate the range of syntactic and semantic constructions, and the inference types, that our system covers.
|
|
| 7. |
- Bernardy, Jean-Philippe, 1978, et al.
(författare)
-
Predicates as Boxes in Bayesian Semantics for Natural Language
- 2019
-
Ingår i: Proceedings of the 22nd Nordic Conference on Computational Linguistics (NoDaLiDa 2019), 30 September-2 October, 2019, Turku, Finland / Mareike Hartmann, Barbara Plank (Editors). - Linköping : Linköping University Electronic Press. - 1650-3686 .- 1650-3740. - 9789179299958
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we present a Bayesian approach to natural language semantics. Our main focus is on the inference task in an environment where judgments require probabilistic reasoning. We treat nouns, verbs, adjectives, etc. as unary predicates, and we model them as boxes in a bounded domain. We apply Bayesian learning to satisfy constraints expressed as premises. In this way we construct a model, by specifying boxes for the predicates. The probability of the hypothesis (the conclusion) is evaluated against the model that incorporates the premises as constraints.
|
|
| 8. |
- Blanck, Rasmus, 1982
(författare)
-
A characterisation of Π₁-conservativity over IΣ₁
- 2016
-
Ingår i: Journées sur les Arithmétiques Faibles 35, 6/6-7/6 2016, Lisbon, Portugal.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- By putting together a number of classic results due to Orey, Hájek, Guaspari and Lindström we get the well known characterisation of Π₁-conservativity over extensions T of Peano arithmetic PA. In short, the following are equivalent for a sentence φ: 1. T + φ is Π₁-conservative over T, 2 T + φ is interpretable in T, 3. for each n ∈ ω, T ⊢ Con(T|n + φ) 4. every model of T can be end-extended to a model of T + φ, 5. every countable model of T can be end-extended to a model of T + φ, 6. for every model M of T, T + Th-Σ₁(M) + φ is consistent. If we instead consider extensions T of IΣ₁, the characterisation breaks down. In this case, neither of 1 or 2 implies the other; we can never have 3 if T is finitely axiomatised; and regarding 4, it is not even known if every model of IΣ₁ has a proper end-extension to a model of IΣ₁. In this talk, which reports on joint work with Ali Enayat, we show that it is possible to salvage parts of this characterisation for extensions of IΣ₁. The equivalence of 1, 5 and 6 can still be shown to hold, and we also present another equivalent condition, which is similar to 3, but phrased in terms of bounded provability.
|
|
| 9. |
- Blanck, Rasmus, 1982
(författare)
-
Contributions to the Metamathematics of Arithmetic: Fixed Points, Independence, and Flexibility
- 2017
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns the incompleteness phenomenon of first-order arithmetic: no consistent, r.e. theory T can prove every true arithmetical sentence. The first incompleteness result is due to Gödel; classic generalisations are due to Rosser, Feferman, Mostowski, and Kripke. All these results can be proved using self-referential statements in the form of provable fixed points. Chapter 3 studies sets of fixed points; the main result is that disjoint such sets are creative. Hierarchical generalisations are considered, as well as the algebraic properties of a certain collection of bounded sets of fixed points. Chapter 4 is a systematic study of independent and flexible formulae, and variations thereof, with a focus on gauging the amount of induction needed to prove their existence. Hierarchical generalisations of classic results are given by adapting a method of Kripke’s. Chapter 5 deals with end-extensions of models of fragments of arithmetic, and their relation to flexible formulae. Chapter 6 gives Orey-Hájek-like characterisations of partial conservativity over different kinds of theories. Of particular note is a characterisation of partial conservativity over IΣ₁. Chapter 7 investigates the possibility to generalise the notion of flexibility in the spirit of Feferman’s theorem on the ‘interpretability of inconsistency’. Partial results are given by using Solovay functions to extend a recent theorem of Woodin.
|
|
| 10. |
- Blanck, Rasmus, 1982
(författare)
-
Fixpunktsmängder : Sets of fixed points
- 2011
-
Ingår i: Filosofidagarna 2011, Göteborg.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Följande föredrag behandlar metamatematiska fixpunkter. Sedan Gödels och Carnaps arbeten i aritmetiserad metamatematik är det känt att varje aritmetisk formel har en fixpunkt. En enkel konsekvens av fixpunktssatsen är att varje aritmetisk formel i själva verket har uppräkneligt många fixpunkter. Vårt grepp är att till varje aritmetisk formel ordna mängden av alla dess fixpunkter och studera dessa mängders egenskaper. I ett antal specialfall kommer även kvantifikatorkomplexiteten hos formler och fixpunkter att begränsas på olika vis. I flertalet fall är dessa mängder fullständiga för rekursivt enumerabla mängder, det vill säga att den rekursionsteoretiska komplexiteten är densamma som för till exempel haltproblemet eller frågan om teoremskap i en r.e. teori. Det intressanta fallet verkar vara dock när en fixpunktsmängd begränsas till att enbart innehålla satser av samma kvantifikatorkomplexitet som den genererande formeln i fråga. Då går det även att finna exempel på rekursiva fixpunktsmängder, och frågan väcks huruvida det finns fixpunktsmängder som varken är rekursiva eller r.e.-fullständiga. Vi presenterar en handfull tillräckliga villkor för rekursivitet respektive r.e.-fullständighet hos fixpunktsmängder, och ger exempel på tänkbara vidare angreppssätt.
|
|
