Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

The acquisition of complex predicates in japanese specifically language-impaired and normally developing children

Japanese exhibits two different types of morphological processes. Some morphologically complex predicates are generated within the domain of the lexicon, whereas others are generated outside the domain of the lexicon. An elicited production task involving both types of complex predicates was administered to six Japanese children with specific language impairment (JSLI) and six children with normal language development (JNLD). The JSLI children experienced significant difficulty forming the lexicon-external complex predicates but much less difficulty with the lexicon-internal complex predicates while the performance of the JNLD children exhibited no such asymmetry. These preliminary results suggest that the deficit of SLI affects the ability to construct implicit procedural rules for morphology that are generated outside the lexicon while their lexical operations for morphology that are generated within the domain of the lexicon remain relatively unimpaired.     

On Conservative Extensions in Logics with Infinitary Predicates

If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for an extension to be conservative. The origin of the results is algebraic logic. Presented by Daniele Mundici Supported by grant OTKA T43242.     

Quantum sortal predicates

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. To Patrick Suppes on his 80th birthday.     

Coordinating perspectives: De se and taste attitudes in communication

The received picture of linguistic communication understands communication as the transmission of information from speaker's head to hearer's head. This picture is in conflict with the attractive Lewisian view of belief as self-location, which is motivated by de se attitudes – first-personal attitudes about oneself – as well as attitudes about subjective matters such as personal taste. In this paper, I provide a solution to the conflict that reconciles these views. I argue for an account of mental attitudes and communication on which mental content and speech act content is understood as sets of multicentered worlds – roughly, possible worlds ‘centered’ on a sequence of individuals at a time. I develop a Stalnakerian model of communication based on multicentered worlds content, and I provide a suitable semantics for personal pronouns and predicates of personal taste. The resulting picture is one on which the point of conversation is the coordination of individual perspectives.     

Relativism and Assertion

Relativism entails that sentences like ‘Liquorice is tasty’ are used to assert relativistic propositions—that is, propositions whose truth-value is relative to a taste standard. I will defend this view against two objections. According to the first objection, relativism is incompatible with a Stalnakerian account of assertion. I will show that this objection fails because Stalnakerian assertions are proposals rather than attempts to update the common ground. According to the second objection, relativism problematically predicts that we can correctly assess beliefs as false but faultless. I will show that it doesn't. Such assessments come out as incorrect because correct relativistic assertion requires the absence of a presupposition of non-commonality.     

Objects, events and "to be" verbs in Spanish--an ERP study of the syntax-semantics interface

In Spanish, objects and events at subject position constrain the selection of different forms of the auxiliary verb “to be”: locative predicates about objects require “estar en”, while those relating to events require “ser en”, both translatable as “to be in”. Subjective ratings showed that while the “object + ser + en” is considered as incorrect, the “event + estar + en” combination is also perceived as unacceptable but to a lesser degree. In an ERP study, we evaluated the impact of a purely semantic distinction (object versus events) on the subsequent processing of these auxiliary verbs followed by locatives in Spanish. For the “ser en” predicate, the P600 component was larger when the subject was an object than when it was an event. This P600 effect is consistent with an online repair of the defining predicate when it does not fit with the adequate semantic properties of the subject. On the other hand, for the “estar en” predicate, event subjects when compared to object subjects showed more positive ongoing amplitudes between 280 and 380 ms after the presentation of the “en” preposition, followed by a longer positive wave starting around 400 ms and lasting until 700 ms after the presentation of the following determiner, with central and frontal scalp distributions respectively. Thus, the different subject-predicate combinations, depending on the semantic features of the subjects, triggered syntactic reparatory processes at a structural level. These findings are consistent with an incremental interpretation of sentence meaning based on the interaction between syntactic and semantic information.     

No Future

The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore arises whether the notions that are investigated in tense logic can be consistently formalized as predicates. In this paper it is shown that the answer to this question is negative. The logical treatment of the notions of future and past as predicates gives rise to paradoxes due the specific interplay between both notions. For this reason, the tense paradoxes that will be presented are not identical to the paradoxes referred to above.     

Cartographic systems and non-linguistic inference

It is often assumed that the capability to make inferences requires language. Against this assumption, I claim that inferential abilities do not necessarily require a language. On the contrary, certain cartographic systems could be used to explain some forms of inferences, and they are capable of warranting rational relations between contents they represent. By arguing that certain maps, as well as sentences, are adequate for inferential processes, I do not mean to neglect that there are important differences between maps and sentences. Instead, the purpose of this paper is to highlight interesting distinctions that might affect the way that cartographic thinking works.     

A Modal Sortal Logic

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.