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## Über dieses Buch

This book constitutes the refereed proceedings of the 10th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2013, held in Gudauri, Georgia, in September 2013. The conference series is centered around the interaction between logic, language and computation. The contributions represent these three fields and the symposia aim to foster interaction between them.

The book consists of 16 papers that were carefully reviewed and selected from 26 submissions. Each paper has passed through a rigorous peer-review process before being accepted for publication. The volume also contains two summaries of the tutorials that took place at the symposium: the one on admissible rules and the one on the formal semantics of aspectual meaning from a cross-linguistic perspective.

## Inhaltsverzeichnis

### Research on Aspect: Reflections and New Frontiers

Abstract
The tutorial gave an overview of the way aspectual meaning has been analyzed in formal semantics. It focused on the way Klein (1994) influential analysis has been extended in recent years to account for the modal properties of aspectual operators. Based on the perfective aspect in Hindi and other languages, I showed that Kleinian extensions which do not view aspectual operators as being partitive with respect to events are inadequate. I explored some consequences of this conclusion and suggested that studying the interface between aspectual and adverbial meaning would allow us to address some of the most pressing issues.
Daniel Altshuler

### Tutorial on Admissible Rules in Gudauri

Abstract
Most theorems have more than one proof and most theories have more than one axiomatization. Certain proofs or axiomatizations are preferable to others because they are shorter or more transparent or for some other reason. Our aim is to describe or study the possible proofs of a theorem or the possible axiomatizations of a theory. As the former is a special instance of the latter, by considering a theory consisting of one theorem, it suffices to consider theories.
Rosalie Iemhoff

### Deontic Conflicts and Multiple Violations

Abstract
This paper presents a novel semantics for deontic modals which provides a uniform solution to prominent puzzles in the literature. The paper focuses on deontic conflicts, discussing them using the Dr. Procrastinate puzzle as an example. The focus lies on the Dr. Procrastinate puzzle as it combines an upward monotonicity puzzle with a conflict of obligations, allowing an explanation of the solutions to both types of puzzle in detail.
The semantics is an extension of radical inquisitive semantics, and it modifies Andersonian deontic modals as it introduces quantification over alternatives. The solution to deontic conflicts is made possible by the semantics allowing permission and prohibition statements to introduce multiple violations. Each rule is assigned a different violation, allowing for reasoning with rules also in cases where it is impossible to avoid violating all rules.
Martin Aher

### Admissibility and Unifiability in Contact Logics

Abstract
Contact logics are logics for reasoning about the contact relations between regular subsets in a topological space. Admissible inference rules can be used to improve the performance of any algorithm that handles provability within the context of contact logics. The decision problem of unifiability can be seen as a special case of the decision problem of admissibility. In this paper, we examine the decidability of admissibility problems and unifiability problems in contact logics.
Philippe Balbiani, Çiğdem Gencer

### F-LTAG Semantics for Issues Around Focusing

Abstract
This paper proposes an analysis in a Feature-based Lexicalized Tree-Adjoining Grammar (F-LTAG) [9, 18] for deriving the semantic representations of various narrow focus constructions. Te paper presents an extension of the F-LTAG analysis by Balogh [3] based on the syntax-semantics approach by Kallmeyer & Romero [11] and the semantic-pragmatic analysis of focus by Balogh [2].
Kata Balogh

### Dialect Dictionaries in the Georgian Dialect Corpus

Abstract
The Georgian Dialect Corpus – GDC (http://​mygeorgia.​ge/​gdc) serves as a source to document and study the regional varieties of the Georgian language. The first steps in terms of the Georgian dialect data collection were taken by Prof. Iost Gippert within his research projects [TITUS, ARMAZI].
The Corpus design strategy on one hand is based on an international corpus linguistics practice and on the other hand on the traditions of the Georgian dialectology and dialectography. The Georgian linguistic and cultural characteristics are being considered in the Corpus design.
The dialect dictionaries are incorporated in the corpus for two reasons: (a) to achieve a high level of representativeness and (b) to use the POS markers of the dictionary lemmas for the morphological annotation of the Corpus. The present paper deals with the practical tasks how these dictionaries complement the dialect lexical fund and how the part of speech markers of the dictionaries are applied in the process of morphological annotation.
Marina Beridze, Liana Lortkipanidze, David Nadaraia

### Duality and Universal Models for the Meet-Implication Fragment of IPC

Abstract
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated universal models of this fragment and give a complete characterization of the up-sets of Kripke models of intuitionistic logic which can be defined by meet-implication-formulas. We use these results to derive a new version of subframe formulas for intuitionistic logic and to show that the uniform interpolants of meet-implication-formulas are not necessarily uniform interpolants in the full intuitionistic logic.
Nick Bezhanishvili, Dion Coumans, Samuel J. van Gool, Dick de Jongh

### Cut-Elimination and Proof Schemata

Abstract
By Gentzen’s famous Hauptsatz (the cut-elimination theorem) every proof in sequent calculus for first-order logic with cuts can be transformed into a cut-free proof; cut-free proofs are analytic and consist entirely of syntactic material of the end-sequent (the proven theorem). But in systems with induction rules, cut-elimination is either impossible or does not produce proofs with the subformula property. One way to overcome this problem is to formulate induction proofs as infinite sequences of proofs in a uniform way and to develop a method, which yields a uniform description of the corresponding cut-free proofs. We present such a formalism, as an alternative to systems with induction rules, and define a corresponding cut-elimination method (based on the CERES-method for first-order logic). The basic tools of proof theory, such as sequent- and resolution calculi are enriched with inductive definitions and schemata of terms, formulas, proofs, etc. We define a class of inductive proofs which can be transformed into this formalism and subjected to schematic cut-elimination.
Cvetan Dunchev, Alexander Leitsch, Mikheil Rukhaia, Daniel Weller

### Towards a Suppositional Inquisitive Semantics

Abstract
One of the primary usages of language is to exchange information. This can be done directly, as in Will Susan sing? No, she won’t, but it is also often done in a less direct way, as in If Pete plays the piano, will Susan sing? No, if Pete plays the piano, Susan won’t sing. In the latter type of exchange, both participants make a certain supposition, and exchange information under the assumption that this supposition holds. This paper develops a semantic framework for the analysis of this kind of information exchange. Building on earlier work in inquisitive semantics, it introduces a notion of meaning that captures informative, inquisitive, and suppositional content, and discusses how such meanings may be assigned in a natural way to sentences in a propositional language. The focus is on conditionals, which are the only kind of sentences in a propositional language that introduce non-trivial suppositional content.
Jeroen Groenendijk, Floris Roelofsen

### Kripke Models Built from Models of Arithmetic

Abstract
We introduce three relations between models of Peano Arithmetic ($$\mathsf {PA}$$), each of which is characterized as an arithmetical accessibility relation. A relation $$\mathrel {R}$$ is said to be an arithmetical accessibility relation if for any model $$\mathcal {M}$$ of $$\mathsf {PA}$$, $$\mathcal {M}\vDash \mathsf {Pr}_{\pi }(\varphi )$$ iff $$\mathcal {M}'\vDash \varphi$$ for all $$\mathcal {M}'$$ with $$\mathcal {M}\mathrel {R}\mathcal {M}'$$, where $$\mathsf {Pr}_{\pi }(x)$$ is an intensionally correct provability predicate of $$\mathsf {PA}$$. The existence of arithmetical accessibility relations yields a new perspective on the arithmetical completeness of $$\mathsf {GL}$$. We show that any finite Kripke model for the provability logic $$\mathsf {GL}$$ is bisimilar to some “arithmetical” Kripke model whose domain consists of models of $$\mathsf {PA}$$ and whose accessibility relation is an arithmetical accessibility relation. This yields a new interpretation of the modal operators in the context of $$\mathsf {PA}$$: an arithmetical assertion $$\varphi$$ is consistent (possible, $$\Diamond \varphi$$) if it holds in some arithmetically accessible model, and provable (necessary, $$\Box \varphi$$) if it holds in all arithmetically accessible models.
Paula Henk

### Positive Formulas in Intuitionistic and Minimal Logic

Abstract
In this article we investigate the positive, i.e. $$\lnot ,\bot$$-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula $$\varphi$$ of IQC we define the positive formula $$\varphi ^+$$ that represents the positive content of $$\varphi$$. The formulas $$\varphi$$ and $$\varphi ^+$$ exhibit the same behavior on top models, models with a largest world that makes all atomic sentences true. We characterize the positive formulas of IPC and IQC as the formulas that are immune to the operation of turning a model into a top model. With the +-operation on formulas we show, using the uniform interpolation theorem for IPC, that both the positive fragment of IPC and MPC respect a revised version of uniform interpolation. In propositional logic the well-known theorem that KC is conservative over the positive fragment of IPC is shown to generalize to many logics with positive axioms. In first-order logic, we show that IQC + DNS (double negation shift) + KC is conservative over the positive fragment of IQC and similar results as for IPC.
Dick de Jongh, Zhiguang Zhao

### Unless and Until: A Compositional Analysis

Abstract
The analyses of unless and until lie at the intersection of logic and linguistics. They crop up in papers about tense connectives [1], quantification [15], anaphora [7], polarity and duality [17, 18] and in classical theorems of tense logic [10]. Unless and until are morphologically similar, and in some contexts, they even appear to be ‘interchangeable’. In this paper we give compositional analyses showing the interrelatedness of these two connectives. In addition, we use this case study to draw some broader methodological points. The locus classicus on the logic of unless is Quine’s Elementary Logic [20] where he sets forth three methodological dogmas. We dub these Quine’s Three Dogmas of Linguistic Negativism and argue that these three dogmas not only give a misleading account of the interplay between logic and linguistics but that rejecting them leads to discovering a unified compositional analysis.
Gary Mar, Yuliya Manyakina, Amanda Caffary

### Frame Theory, Dependence Logic and Strategies

Abstract
We present a formalization of the Löbner-Barsalou frame theory (LBFT) in Dependence Logic with explicit strategies. In its present formalization, [Pet07], frames are defined as a particular kind of typed feature structures. On this approach, the semantic value of a lexical item is reduced to its contribution to the truth conditions of sentences in which it occurs. This reduction does neither account for dynamic phenomena nor for results from neuroscience which show that meaning cannot be reduced to truth conditions. In order to overcome these shortcomings, we develop a dynamic frame theory which is based both on Dependence Logic [Vää07] and Dynamic Epistemic Logic ([vB11]). The semantic phenomenon with respect to which this framework is tested are numerical expressions like ‘two’ or ‘at least two’. They are interpreted as strategies which change the input information state to which they are applied.
Ralf Naumann, Wiebke Petersen

### Uniqueness and Possession: Typological Evidence for Type Shifts in Nominal Determination

Abstract
This paper highlights the analogy of definiteness and possession by utilising the distinction between semantic and pragmatic uniqueness as outlined in Löbner’s (2011) Concept Type and Determination approach. Assuming, on the basis of the features [$$\pm$$ unique] and [$$\pm$$ relational], a classification into the four logical types sortal, relational, individual, and functional concept, nouns will be used either in congruence with or deviating from their underlying type. I present evidence from Germanic and Mayan languages for the following claims: (1) noun uses that deviate from the underlying type tend to be reflected by overt morphology; (2) in article split languages, phonologically ‘strong’ forms indicate pragmatic uniqueness, thus, denote a function from [$$-$$ unique] to [+ unique], whereas ‘weak’ forms tend to be semantically redundant. Regarding possession, ‘alienable’ morphology denotes a function from non-relational to relational (pragmatic possession), whereas ‘inalienable’ morphology is restricted to semantic possession. Overall, split systems imply a strong correlation between conceptual markedness and morphosyntactic markedness.
Albert Ortmann

### Alternative Semantics for Visser’s Propositional Logics

Abstract
Visser’s basic propositional logic $$\mathbf {BPL}$$ is the subintuitionistic logic determined by the class of all transitive Kripke frames, and his formal provability logic $$\mathbf {FPL}$$, an extension of $$\mathbf {BPL}$$, is determined by the class of all irreflexive and transitive finite Kripke frames. While Visser showed that $$\mathbf {FPL}$$ is embeddable into the modal logic $$\mathbf {GL}$$, we first show that $$\mathbf {BPL}$$ is embeddable into the modal logic $$\mathbf {wK4}$$, which is determined by the class of all weakly transitive Kripke frames, and we also show that $$\mathbf {BPL}$$ is characterized by the same frame class. Second, we introduce the proper successor semantics under which we prove that $$\mathbf {BPL}$$ is characterized by the class of weakly transitive frames, transitive frames, pre-ordered frames, and partially ordered frames. Third, we introduce topological semantics by interpreting implication in terms of the co-derived set operator and prove that $$\mathbf {BPL}$$ is characterized by the class of all topological spaces, $$T_0$$-spaces and $$T_d$$-spaces. Finally, we establish the topological completeness of $$\mathbf {FPL}$$ with respect to the class of scattered spaces.
Katsuhiko Sano, Minghui Ma

### Between-Noun Comparisons

Abstract
Adjectives are typically felicitous in within-predicate comparisons—constructions of the form ‘X is more A than y’, as in This is bigger than that, but are often infelicitous in between-predicate comparisons—‘X is more A than (y is) B’, as in *Tweety is bigger than (it is) heavy. Nouns, by contrast, exhibit the inverse pattern. The challenge is to account for the felicity of between-noun comparisons, such as more a duck than a goose, while capturing the infelicity of within-noun comparisons, such as #This bird is more a duck than that one. Postulating even only ad hoc, meta-linguistic gradable interpretations for noun to capture the meaning of between-noun comparisons results in wrong predictions for within-noun comparisons and other gradable constructions (#very duck; too duck). To address this challenge, the paper exploits the psychological notion of a contrast-set. The solution correctly predicts inference patterns and truth value judgments.
Galit W. Sassoon

### On the Licensing of Argument Conditionals

Abstract
The paper focusses on the syntactic and semantic licensing conditions of constructions like Max akzeptiert es, wenn Lea Geige spielt. ‘Max accepts it if Lea plays the violin’. The clause introduced by wenn ‘if’ has a double function in that it is an adverbial that provides the protasis of an implication as well as the propositional argument of a matrix predicate. The paper argues against Pullum [15], Pesetsky [14], and Hinterwimmer [8], suggesting that the conditional conjunction wenn encodes two implication types: the classic type: if p is contingent and true, then q(p) and the preference type: if p is contingent, then q(p). Additionally, the paper focusses on the characteristic properties of the matrix predicates that license argument conditionals.
Kerstin Schwabe

### Biaspectual Verbs: A Marginal Category?

Abstract
The hallmark property of the Russian verbal system is taken to be the bipartite perfective/imperfective distinction in the domain of grammatical aspect. In this paper we show that there is a substantial and productive class of morphologically complex verbs that do not clearly pattern as either perfective or imperfective on standard formal (distributional) tests for perfectivity versus imperfectivity. Such verbs also pose problems for contemporary syntactic approaches to Russian complex verbs. The main innovation we propose is a new positive test for perfectivity which, along with the standard formal (distributional) tests, allows us to provide empirical evidence for the existence of a class of verbs that exhibit a variable grammatical aspect behavior, i.e., behave like perfective or imperfective verbs in dependence on context. Apart from shedding a new light on the standard tests for the aspectual membership of Russian verbs, the main empirical outcome seems to suggest that a third–biaspectual–class of verbs which cannot be neatly aligned with either the perfective or imperfective class must be recognized. This immediately raises the question about its status with respect to the traditional bipartite perfective/imperfective distinction.
Yulia Zinova, Hana Filip

### Backmatter

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