A logic for reasoning about knowledge of unawareness

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of” – without using a stronger statement such as “Ann knows that Bill is aware of p and Ann is not aware of p”, for some particular p. In Halpern and Rêgo (2006, 2009b) (revisited in Halpern and Rêgo (2009a, 2013)) Halpern and Rêgo introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (2006, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete

Depth-bounded Epistemic Logic

Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an extension of S5 that models agents that can reason about epistemic formulas only up to a specific modal depth. To support explicit reasoning about agent depths, DBEL includes depth atoms Ead (agent a has depth exactly d) and Pad (agent a has depth at least d). We provide a sound and complete axiomatization of DBEL. We extend DBEL to support public announcements for bounded depth agents and show how the resulting DPAL logic generalizes standard axioms from public announcement logic. We present two alternate extensions and identify two undesirable properties, amnesia and knowledge leakage, that these extensions have but DPAL does not. We provide axiomatizations of these logics as well as complexity results for satisfiability and model checking. Finally, we use these logics to illustrate how agents with bounded modal depth reason in the classical muddy children problem, including upper and lower bounds on the depth knowledge necessary for agents to successfully solve the problem.Comment: In Proceedings TARK 2023, arXiv:2307.0400

A ternary knowledge relation on secrets

ABSTRACT The paper introduces and studies the ternary relation "secret a reveals at least as much information about secret c as secret b ." In spite of its seeming simplicity, this relation has many non-trivial properties. The main result is a complete infinite axiomatization of the propositional theory of this relation

Kielen tunnistus koneoppimismenetelmillä

Koneoppimismenetelmien avulla aineistosta voidaan irrottaa piirteitä ja luokitella se eri luokkiin näiden piirteiden perusteella. Erilaisia piirteenirrotus- ja luokittelumenetelmiä hyödyntämällä on mahdollista esimerkiksi tunnistaa kirjoitetusta tekstistä sen kieli. Tässä työssä esitellään erilaisia ohjattua oppimista käyttäviä koneoppimismenetelmiä ja kokeillaan niiden soveltuvuutta kielen tunnistamiseen. Työssä käytettyjä piirteenirrotusmenetelmiä ovat TF-IDF ja n-gram, kun taas luokitteluun käytettyihin menetelmiin kuuluvat random forest, logistinen regressio ja tukivektorikone. Algoritmien esittelemisen lisäksi käydään vaihe kerrallaan läpi kielen tunnistuksessa tapahtuva koneoppimisprosessi. Työssä esitetään testauksen tulokset ja niiden pohjalta jokaisen menetelmän suoriutumista arvioidaan. Tutkimuksen perusteella nähdään, että kaikki tässä työssä käsitellyt piirteenirrotus- ja luokittelumenetelmät soveltuvat hyvin tekstin luokitteluun kirjoituskielen perusteella