139 research outputs found
Modeling Nonintersective Adjectives Using Operator Logics
Our topic is one that involves the interface between natural language and mathematical logic. First-order predicate language/logic does a good job approximating many parts of (English) speech, i.e., nouns, verbs and prepositions, but fails decidedly when it comes to, say, adjectives. In particular, it cannot account for the quite different ways in which the adjectives green and big modify a noun such as chair. In the former case, we can easily view a world in which the class of green chairs is the intersection of the class of green things with the class of chair-things. By contrast, the way big modifies a noun depends on the noun itself: a big chair is microscopic when compared to the smallest of galaxies. We investigate logical languages inspired by this phenomenon; particularly those with variables ranging over individuals and with variable-binding operators akin to generalized quantifiers
Modal Hybrid Logic
This is an extended version of the lectures given during the 12-th Conference on Applications of Logic in Philosophy and in the Foundations of Mathematics in Szklarska Poręba (7–11 May 2007). It contains a survey of modal hybrid logic, one of the branches of contemporary modal logic. In the first part a variety of hybrid languages and logics is presented with a discussion of expressivity matters. The second part is devoted to thorough exposition of proof methods for hybrid logics. The main point is to show that application of hybrid logics may remarkably improve the situation in modal proof theory
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On the Logic of Belief and Propositional Quantification
We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is some-thing that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator (BAOs) validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. Hence, by duality, we also cover the usual method of adding propositional quantifiers to normal modal logics by considering their classes of Kripke frames. In addition, we obtain decidability for all the concrete logics we discuss
Worlds and Objects of Epistemic Space : A study of Jaakko Hintikka's modal semantics
This study focuses on meaning and knowledge by assessing a distinctive view
regarding their relation, namely the modal view of Jaakko Hintikka. The
development of this view has not been previously scrutinized. By paying close
attention to the texts of Hintikka, I show that, despite the extensive deployment of
mathematical tools, the articulation of the view remained intuitive and vague. The
study calls attention to several points at which Hintikka omits relevant details or
disregards foundational questions. Attempts are made to articulate Hintikka’s
certain ideas in a more specific manner, and new problems that result are
identified. The central claim argued for is that Hintikka’s exposition was
unsatisfactory in many respects and hence the view, as it stands, falls short in its
explanatory scope compared to current theories in the intersection of logic,
semantics, and epistemology. However, I argue that, despite its shortcomings, the
prospects of the modal view are not exhausted. This is verified by introducing a
new interpretation of the framework and by sketching new applications relevant in
philosophy of language and in epistemology. It is also pointed out that certain
early advances of the view closely resemble, and therefore anticipate, the central
tenets of the currently influential two-dimensional approaches in logic and
semantics.Tutkimus paneutuu merkityksen ja tiedon käsitteisiin tarkastelemalla Jaakko Hintikan työtä modaalisen semantiikan parissa. Tutkimus osoittaa, että Hintikka jätti modaalisen semantiikan kehitystyössään avoimeksi useita perustavia kysymyksiä ja yksityiskohtia. Tutkimuksessa pyritään artikuloimaan täsmällisemmin joitakin Hintikan näkemyksiä, ja tunnistetaan uusia syntyviä ongelmia. Keskeisenä väitteenä on, että Hintikan teoreettinen työ jäi monilta osin epätyydyttäväksi, ja siten hänen modaalinen näkemyksensä ei yllä selitysvoimaltaan ja sovelluspotentiaaliltaan samalle tasolle kuin nykyiset filosofiset teoriat, jotka operoivat logiikan, semantiikan ja epistemologian risteyskohdissa. Tästä huolimatta tutkimuksessa argumentoidaan, että Hintikan teoreettinen viitekehys tarjoaa myös uusia kiinnostavia näköaloja. Tämä todennetaan tarjoamalla Hintikan viitekehykselle uusi tulkinta, ja soveltamalla sitä uusiin kielifilosofisiin kysymyksiin. Tutkimus nostaa myös esiin kirjallisuudessa ohitetun tosiasian, että Hintikan työ ennakoi tärkeällä tavalla nykyisin vaikutusvaltaisia kaksi-dimensionaalisia lähestymistapoja logiikassa ja semantiikassa
Nominal tense logic and other sorted intensional frameworks
This thesis introduces of a system of tense logic called nominal tense logic (NTL), and
several extensions. Its primary aim is to establish that these systems are logically interesting,
and can provide useful models of natural language tense, temporal reference, and
their interaction.
Languages of nominal tense logic are a simple augmentation of Priorean tense logic.
They add to the familiar Priorean languages a new sort of atomic symbol, nominals. Like
propositional variables, nominals are atomic sentences and may be freely combined with
other wffs using the usual connectives. When interpreting these languages we handle the
Priorean components standardly, but insist that nominals must be true at one and only
one time. We can think of nominals as naming this time.
Logically, the change increases the expressive power of tensed languages. There are
certain intuitions about the flow of time, such as irreflexivity, that cannot be expressed
in Priorean languages; with nominals they can. The effects of this increase in expressive
power on the usual model theoretic results for tensed languages discussed, and completeness
and decidability results for several temporally interesting classes of frames are
given. Various extensions of the basic system are also investigated and similar results
are proved. In the final chapter a brief treatment of similarly referential interval based
logics is presented.
As far as natural language semantics is concerned, the change is an important one. A
familiar criticism of Priorean tense logic is that as it lacks any mechanism for temporal
reference, it cannot provide realistic models of natural language temporal usage. Natural
language tense is at least partly about referring to times, and nowadays the deictic and
anaphoric properties of tense are a focus of research. The thesis presents a uniform treatment
of certain temporally referring expressions such as indexicals, and simple discourse
phenomena
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