Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz’s 3-valued Logic Ł3

?ukasiewicz three-valued logic ?3 is often understood as the set of all 3-valued valid formulas according to ?ukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of ?3: “well-determined” ?3a and “truth-preserving” ?3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for ?3, ?3a and ?3b. The logic ?3 is axiomatized as an extension of Routley and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” ?ukasiewicz logics are paraconsistent.     

A Peculiarity in Pearl’s Logic of Interventionist Counterfactuals

We examine a formal semantics for counterfactual conditionals due to Judea Pearl, which formalizes the interventionist interpretation of counterfactuals central to the interventionist accounts of causation and explanation. We show that a characteristic principle validated by Pearl’s semantics, known as the principle of reversibility, states a kind of irreversibility: counterfactual dependence (in David Lewis’s sense) between two distinct events is irreversible. Moreover, we show that Pearl’s semantics rules out only mutual counterfactual dependence, not cyclic dependence in general. This, we argue, suggests that Pearl’s logic is either too weak or too strong.     

Existential Import in Cartesian Semantics

The paper explores the existential import of universal affirmative in Descartes, Arnauld and Malebranche. Descartes holds, inconsistently, that eternal truths are true even if the subject term is empty but that a proposition with a false idea as subject is false. Malebranche extends Descartes’ truth-conditions for eternal truths, which lack existential import, to all knowledge, allowing only for non-propositional knowledge of contingent existence. Malebranche's rather implausible Neoplatonic semantics is detailed as consisting of three key semantic relations: illumination by which God's ideas cause mental terms, creation by which God's ideas cause material substances by a kind of ‘ontic privation’, and sensation in which brain events occasion states of mental awareness. In contrast, Arnauld distinguishes two types of propositions – necessary and contingent – with distinct truth-conditions, one with and one without existential import. Arnauld's more modern semantics is laid out as a theory of reference that substitutes earlier causal accounts with one that adapts the medieval notion of objective being. His version anticipates modern notions of intentional content and appeals in its ontology only to substances and their modes.     

Preferential Semantics using Non-smooth Preference Relations

This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation ? . They are equivalent to Shoham’s so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After discussing this type of semantics, we focus on some concrete proposals from the literature, checking a number of meta-theoretic properties and elaborating on their intuitive motivation. As it turns out, many of their meta-properties only hold in case ? is transitive. To tackle this problem, we propose slight modifications of each of the systems, showing the resulting logics to behave better at the intuitive level and in metatheoretic terms, for arbitrary ? .     

Husserl on Meaning,Grammar, and the Structure of Content

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, it is not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations (both mental and linguistic) contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this  account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system.     

Prescribed spatial prepositions influence how we think about time

Prepositions combine with nouns flexibly when describing concrete locative relations (e.g. at/on/in the school) but are rigidly prescribed when paired with abstract concepts (e.g. at risk; on Wednesday; in trouble). In the former case they do linguistic work based on their discrete semantic qualities, and in the latter they appear to serve a primarily grammatical function. We used the abstract concept of time as a test case to see if specific grammatically prescribed prepositions retain semantic content. Using ambiguous questions designed to interrogate one’s meaningful representation of temporal relations, we found that the semantics of prescribed prepositions modulate how we think about time. Although prescribed preposition use is unlikely to be based on a core representational organization shared between space and time, results demonstrate that the semantics of particular locative prepositions do constrain how we think about paired temporal concepts.     

A Lewisian Semantics for S2

This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory.     

Singular troubles with singleton socrates

I identify a problem for Kit Fine’s truthmaker semantics for ground: it excludes a range of plausible structures of grounding hierarchies. Specifically, there is an attractive view about the grounds of the existence of individual singleton sets which is inconsistent under the truthmaker account. I then develop a modification of the truthmaker account which avoids this difficulty and show that it preserves most of the desirable features of the original account, such as the propositional logic of ground it yields.     

Hintikka’s Independence-Friendly Logic Meets Nelson’s Realizability

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics (abbreviated GTS) for independence-friendly first-order logic (IF-FOL), but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas.     

Referential Dependencies Between Conflicting Attitudes

A number of puzzles about propositional attitudes in semantics and philosophy revolve around apparent referential dependencies between different attitudes within a single agent’s mental state. In a series of papers, Hans Kamp (2003… 2015) offers a general framework for describing such interconnected attitude complexes, building on DRT and dynamic semantics. I demonstrate that Kamp’s proposal cannot deal with referential dependencies between semantically conflicting attitudes, such as those in Ninan’s (21) puzzle about de re imagination. To solve the problem I propose to replace Kamp’s treatment of attitudes as context change potentials with a two-dimensional analysis.     

Rosy with Sider? The Case of the Metaphysical Liar

An important trend in contemporary metaphysics denies that the structure of natural language is an important datum for investigating fundamental structure. Ted Sider proceeds on this basis to propose a metaphysical semantics for natural language. Within this framework he argues that natural language and a fundamental, ‘jointcarving’, language could be subject to distinct logics. Developing an argument of Hartry Field’s, I show that Sider’s preferred option of fundamental classicality combined with non-fundamental non-classicality trivialises within the framework of Siderian metaphysical semantics. The position can be saved only by revising key claims about truth and metaphysical semantics. This has serious implications for methdology in the metaphysics of logic.     

How language relates to belief,desire, and emotion understanding

Two experiments examined syntax and semantics as correlates of theory-of-mind (ToM). In Experiment 1 children’s language was examined at 3 years of age in relation to ToM at 3, 3.5, 4, and 5.5 years. Semantics predicted unique variance in later belief understanding but not desire understanding. Syntax did not explain unique variance in belief or desire. In Experiment 2 two measures of syntax and a measure of semantics were used with 65 3–5-year-olds. The syntax measures tested children’s understanding of word order and embedded clauses. They were related to false belief, but contrary to some predictions, were also related to emotion recognition. Performance on language control tasks with low syntactic demands correlated equally well with false belief. In both experiments performance on the syntax and semantics tasks was highly inter-correlated. We argue that ToM is related to general language ability rather than syntax or semantics per se.     

A Closer Look at Manifest Consequence

Fine (2007) argues that Frege’s puzzle and its relatives demonstrate a need for a basic reorientation of the field of semantics. According to this reorientation, the domain of semantic facts would be closed not under the classical consequence relation but only under a stronger relation Fine calls “manifest consequence.” I examine Fine’s informally sketched analyses of manifest consequence, showing that each can be amended to determine a class of strong consequence relations. A best candidate relation emerges from each of the two classes, and I prove that the two candidates extensionally coincide. The resulting consequence relation is of independent interest, for it might be held to constitute a cogent standard of reasoning that proceeds under a deficient grasp on the identity of objects.     

Reasoning with prioritized information by iterative aggregation of distance functions

We introduce a general framework for reasoning with prioritized propositional data by aggregation of distance functions. Our formalism is based on a possible world semantics, where conclusions are drawn according to the most ‘plausible’ worlds (interpretations), namely: the worlds that are as ‘close’ as possible to the set of premises, and, at the same time, are as ‘faithful’ as possible to the more reliable (or important) information in this set. This implies that the consequence relations that are induced by our framework are derived from a pre-defined metric on the space of interpretations, and inferences are determined by a ranking function applied to the premises. We study the basic properties of the entailment relations that are obtained by this framework, and relate our approach to other methods of maintaining incomplete and inconsistent information, most specifically in the contexts of (iterated) belief revision, consistent query answering in database systems, and integration of prioritized data sources.     

Chinese Children’s Knowledge of Topicalization: Experimental Evidence from a Comprehension Study

There is a debate as to whether topic structures in Chinese involve A’-movement or result from base-generation of the topic in the left periphery. If Chinese topicalization was derived by movement, under the assumptions of Friedmann et al.’s Relativized Minimality (Lingua 119:67–88, 2009), we would expect children’s comprehension of object topicalization (with OSV order) to be worse than their comprehension of subject topicalization (with SVO order). This study examined 146 Mandarin-speaking children from age three to age six by means of a picture-sentence matching task with an appropriate context. The results showed a subject/object asymmetry when the topic marker is overt, and no asymmetry when the topic marker is covert. This suggests that the presence or absence of topic markers play an important role in children’s comprehension of topicalization. We propose that both structures involve movement in the adult grammar, but not in the child grammar, at least initially. Sentences without overt topic markers are base-generated on a par with gapless sentences with a topic, and the base-generation analysis is abandoned as soon as children learn the syntax and semantics of topic markers, which function as attractors of topics.     

Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information

We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.     

动词体的球态语义学

本文介绍由塔斯基的立体几何导出的球态语义学,并将其应用于自然语言中的动词体现象。球态语义学特别适合应用于英语的进行体。这种方法有以下优点（i）它扩展了区间式语义,并同时避免了其缺陷,（ii）它解决了未完成体难题,（iii）它的解决方法无需诉诸最终结果策略。逻辑方法一般被认为难于处理自然语言的动词体问题。基于点的时间结构以及建立在该结构之上的经典普莱尔时态逻辑（[18]）太弱了。而基于区间的时态语义则缺乏足够的表达力,并且难以解释进行体（[4,8]）.本文给出一种新的基于球上整体－部分关系概念的模型和时态语义。这种球态语义学建基于塔斯基1927年引入的立体几何之上。与基于点和基于区间的语义不同,在球态语义学中很多动词体区分都由统一的逻辑方法刻画。在一个由封闭球构成的论域中,可达关系由相切性概念给出。相应地,我们可定义外切、内切、外径、内径以及同心等基本概念。与区间式语义不同,球是论域的初始概念,球态语义学不是在时间段而是在球中对事件赋值。因此,仅将时间区间作为初始概念而不承认其端点初性性的问题不复存在。英语中的进行体由球上的连续行动来刻画。行动是非终止的,只要球没有由外切相离。相应地,外切相离刻车动作完成。我们区分在均匀球和非均匀球中发生事件的整体-部分关系。非持续动作视为直径为零的同心球。球态语义学根据动作或执行完成的时刻来定义时间概念,其中不需要时间端点的概念。在保持与基于区间的时间模型类似的基础上,球态语义学暗示了一种关于可能世界的定性概念,并且它有利于解决时间的循环概念问题。     

Shifty characters

In “Demonstratives”, David Kaplan introduced a simple and remarkably robust semantics for indexicals. Unfortunately, Kaplan’s semantics is open to a number of apparent counterexamples, many of which involve recording devices. The classic case is the sentence “I am not here now” as recorded and played back on an answering machine. In this essay, I argue that the best way to accommodate these data is to conceive of recording technologies as introducing special, non-basic sorts of contexts, accompanied by non-basic conventions governing the use of indexicals in those contexts. The idea is that recording devices allow us to use indexicals in new and innovative ways to coordinate on objects. And, given sufficient regularity in the use of indexicals on such devices, linguistic conventions will, over time, come to reflect this innovation. I consider several alternatives to this ‘character-shifting’ theory, but none is able to account for the data as well as the present proposal. Many face additional theoretical difficulties as well. I conclude by explaining how the character-shifting theory not only retains many of the virtues of Kaplan’s original semantics, but also coheres with a plausible view on the nature of semantic theorizing more generally.     

Depth of intention

The paper attempts to reconstruct some notions of Naess's semantics, and at the same time to relate them to more recent developments. On Naess's view, there is no such thing as a language in the sense of a shared structure which determines clear‐cut literal meanings like Fregean Gedanken or propositions. We use words, and try to interpret each other; but there is no a priori or intuitive basis for secure and precise knowledge about language. Interpretation or understanding, as well as thinking and perception, involve discrimination at higher or lower levels. There is neither a ceiling of crystal‐clear propositions nor a floor of ‘given’ sensations or ‘objective’ stimuli independent of categorizations and discriminations, which might serve as a bridge for translation or interpretation between the conceptual‐perceptual schemes of individuals. The notions of ‘concept’, ‘conceptual framework’, ‘situation’, ‘situation type’ and ‘proposition’ are defined, with some reliance on Barwise and Perry's situation semantics. Two notions of accessibility of situation types are defined; one as constructibility of the type at a given level of discrimination, i.e. in terms of objects discerned and concepts discriminated; the other as intelligibility of the type. Intelligibility entails constructibility, but not conversely. A type of situation may be constructible at some person's level of discrimination, but not coherently intelligible to him. On this basis, a logic of senses or truth‐conditions for uses of expressions is developed, and a logic of interpretations of uses. The central notions of Naessian semantics are defined: ambiguity and direction of interpretation, level of discrimination and depth of intention.