Showing papers in "Journal of Logic, Language and Information in 2021"
TL;DR: In this paper, the authors consider coalition announcements through the lens of group announcements and provide a complete axiomatisation of a logic with coalition announcements, and study some logical properties of both coalition and group announcements that have not been studied before.
Abstract: There are several ways to quantify over public announcements. The most notable are reflected in arbitrary, group, and coalition announcement logics (APAL, GAL, and CAL correspondingly), with the latter being the least studied so far. In the present work, we consider coalition announcements through the lens of group announcements, and provide a complete axiomatisation of a logic with coalition announcements. To achieve this, we employ a generalisation of group announcements. Moreover, we study some logical properties of both coalition and group announcements that have not been studied before.
8 citations
TL;DR: This paper presents an introduction to the notions of incrementality and underspecification and update, drawing on the assumptions made by Dynamic Syntax, in order to understand the accounts developed in the other contributions to the Special Issue.
Abstract: Dynamic Syntax (DS: Kempson et al. 2001; Cann et al. 2005) is an action-based grammar formalism which models the process of natural language understanding as monotonic tree growth. This paper presents an introduction to the notions of incrementality and underspecification and update, drawing on the assumptions made by DS. It lays out the tools of the theoretical framework that are necessary to understand the accounts developed in the other contributions to the Special Issue. It also represents an up-to-date account of the framework, combining the developments that have previously remained distributed in a diverse body of literature.
6 citations
TL;DR: A proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser shows that categorial grammars based on them can generate arbitrary recursively enumerable languages.
Abstract: We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative (Lambek) connectives, additive conjunction and disjunction, brackets and bracket modalities, and the ! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut (cut elimination theorem). We also prove algorithmic undecidability for both calculi, and show that categorial grammars based on them can generate arbitrary recursively enumerable languages.
5 citations
TL;DR: In this paper, the authors define the $$\mathsf {ClAnt}$$====== fragment of the first-order logic and prove its strong completeness with respect to axiomatization.
Abstract: Inquisitive first order logic is an extension of first order classical logic, introducing questions and studying the logical relations between questions and quantifiers. It is not known whether is recursively axiomatizable, even though an axiomatization has been found for fragments of the logic (Ciardelli, 2016). In this paper we define the $$\mathsf {ClAnt}$$
—classical antecedent—fragment, together with an axiomatization and a proof of its strong completeness. This result extends the ones presented in the literature and introduces a new approach to study the axiomatization problem for fragments of the logic.
4 citations
TL;DR: A PSPACE-complete model checking algorithm for CAL that produces winning strategies for coalitions and is implemented in a proof-of-concept model checker.
Abstract: Coalition announcement logic (CAL) is one of the family of the logics of quantified announcements. It allows us to reason about what a coalition of agents can achieve by making announcements in the setting where the anti-coalition may have an announcement of their own to preclude the former from reaching its epistemic goals. In this paper, we describe a PSPACE-complete model checking algorithm for CAL that produces winning strategies for coalitions. The algorithm is implemented in a proof-of-concept model checker.
3 citations
TL;DR: This article proposes that the parse of a case particle maximally excludes potential landing sites of an unfixed nodes at the time of parsing the case particle, delaying the resolution of the unfixed node until a subsequent stage of structure building.
Abstract: ‘Case’ and ‘grammatical relations’ are central to syntactic theory, but rigorous treatments of these concepts in surface-oriented grammars such as Dynamic Syntax are pending. In this respect, Japanese is worthy of mention; in this language, the nominative case particle ga, which typically marks a subject, may mark an object in certain syntactic contexts, and more than one instance of ga may be present within a single clause. These patterns cannot be captured if we simply assume that ga marks a subject. In the present article, we aim to advance formal aspects of the framework, especially the mechanism of ‘structural underspecification,’ by proposing that the parse of a case particle maximally excludes potential landing sites of an unfixed node at the time of parsing the case particle, delaying the resolution of the unfixed node until a subsequent stage of structure building. This maximal exclusion approach to structural underspecification accounts for a range of case marking patterns and their connections with grammatical relations.
3 citations
TL;DR: This paper argues that this framework capable of dealing with anaphora and ellipsis can provide a unified account of a large number of anaphoric phenomena and uses Haskell as a meta-language to present the theory, which also consitutes an implementation of all the phenomena discussed.
Abstract: In this paper, we propose a framework capable of dealing with anaphora and ellipsis which is both general and algorithmic. This generality is ensured by the compination of two general ideas. First, we use a dynamic semantics which reperent effects using a monad structure. Second we treat scopes flexibly, extending them as needed. We additionally implement this framework as an algorithm which translates abstract syntax to logical formulas. We argue that this framework can provide a unified account of a large number of anaphoric phenomena. Specifically, we show its effectiveness in dealing with pronominal and VP-anaphora, strict and lazy pronouns, lazy identity, bound variable anaphora, e-type pronouns, and cataphora. This means that in particular we can handle complex cases like Bach–Peters sentences, which require an account dealing simultaneously with several phenomena. We use Haskell as a meta-language to present the theory, which also consitutes an implementation of all the phenomena discussed in the paper. To demonstrate coverage, we propose a test suite that can be used to evaluate computational approaches to anaphora.
3 citations
TL;DR: In this article, Gentzen-type sequent calculi BDm and BDi for a modal extension and an intuitionistic modification, respectively, of De and Omori's extended Belnap-Dunn logic BD+ with classical negation were introduced.
Abstract: In this study, we introduce Gentzen-type sequent calculi BDm and BDi for a modal extension and an intuitionistic modification, respectively, of De and Omori’s extended Belnap–Dunn logic BD+ with classical negation. We prove theorems for syntactically and semantically embedding BDm and BDi into Gentzen-type sequent calculi S4 and LJ for normal modal logic and intuitionistic logic, respectively. The cut-elimination, decidability, and completeness theorems for BDm and BDi are obtained using these embedding theorems. Moreover, we prove the Glivenko theorem for embedding BD+ into BDi and the McKinsey–Tarski theorem for embedding BDi into BDm.
3 citations
TL;DR: In this paper, the authors combine propositional dynamic logic (PDL) with propositional inquisitive logic (InqB) to obtain a logical system that conservatively extends both PDL and InqB.
Abstract: This paper combines propositional dynamic logic (
$${\textsf {PDL}}$$
) with propositional inquisitive logic (
$$\textsf {InqB}$$
). The result of this combination is a logical system $$\textsf {InqPDL}$$
that conservatively extends both $${\textsf {PDL}}$$
and $$\textsf {InqB}$$
, and, moreover, allows for an interaction of the question-forming operator from $$\textsf {InqB}$$
with the structured modalities from $${\textsf {PDL}}$$
. We study this system from a semantic as well as a syntactic point of view. These two perspectives are linked via a completeness proof, which also shows that $$\textsf {InqPDL}$$
is decidable.
3 citations
TL;DR: This article presented a corpus study of acknowledgements and clarification requests in British English, and describe how their low-level, semantic processing model in Dynamic Syntax accounts for this feedback, which can be integrated or interpreted at non-FRSs using the predictive, incremental and interactive nature of the formalism.
Abstract: Feedback such as backchannels and clarification requests often occurs subsententially, demonstrating the incremental nature of grounding in dialogue. However, although such feedback can occur at any point within an utterance, it typically does not do so, tending to occur at Feedback Relevance Spaces (FRSs). We present a corpus study of acknowledgements and clarification requests in British English, and describe how our low-level, semantic processing model in Dynamic Syntax accounts for this feedback. The model trivially accounts for the 85% of cases where feedback occurs at FRSs, but we also describe how it can be integrated or interpreted at non-FRSs using the predictive, incremental and interactive nature of the formalism. This model shows how feedback serves to continually realign processing contexts and thus manage the characteristic divergence and convergence that is key to moving dialogue forward.
2 citations
TL;DR: In this article, the authors argue that the appeal to standard set theory in (mainstream) minimalist syntax is in conflict with the goal of analyzing dependency formation, a.k.a. movement, as involving genuine constituent copies.
Abstract: Appeal to standard set theory in (mainstream) minimalist syntax is shown to be in conflict with the goal of analyzing dependency formation, a.k.a. movement, as involving genuine constituent copies. The underlying tension is due to (the axiom of) extensionality, which—other things being equal—favors a perspective on dependencies in terms of multidominance. The above argument is developed against the backdrop of a recent exposition of minimalist syntax (Chomsky et al. in Catal J Linguist (Special Issue):229–261, 2019), which can be seen as exemplary. The resulting critical assessment should be taken as removing obstacles on the way toward proper minimalist foundations for syntactic theory.
TL;DR: This paper argues that the transition from Koine Greek to the Medieval varieties and from theieval varieties to the respective modern ones can be explained by making the assumption that routinisation and parsing/hearer assymetries are two important factors behind syntactic change.
Abstract: In this paper, the historical development of the clitic systems of Standard Modern, Cypriot and Pontic Greek is discussed. These three varieties not only present the whole range of variation one can find across clitic systems in Greek but, furthermore, derive from a common linguistic ancestor, i.e. Koine Greek. This paper argues that the transition from Koine Greek to the Medieval varieties and from the Medieval varieties to the respective modern ones can be explained by making the assumption that routinisation (in the sense of Pickering and Garrod in Behav Brain Sci 27:169–226, 2004) and parsing/hearer assymetries are two important factors behind syntactic change. The claim is that the transition from Koine to the Medieval Greek varieties involves the emergence of a clitic system with encoded syntactic constraints out of a freer one, where clitic positioning was regulated by pragmatic preferences rather than syntactic constraints. Then, the transition to the modern varieties from the respective medieval ones is explained, at least partly, on the assumption that production/parsing mismatches are capable of triggering syntactic change. This last assumption combined with: (a) the tendency to obtain more generalised parsing triggers for parsing the individual clitics and (b) the fact that the Medieval varieties in question differ in minimal but crucial ways, provides us an explanation for the transition to the modern varieties.
TL;DR: The problem of non-zero probabilities for non-tautologous universal generalizations in Rudolf Carnap’s inductive logic when the domain of discourse is infinite is discussed.
Abstract: This article discusses the problem of non-zero probabilities for non-tautologous universal generalizations in Rudolf Carnap’s inductive logic (1950, 1952) when the domain of discourse is infinite. A solution is provided for a generalization of the form “all Xs are Ys”, for example “all ravens all black”. The solution is based on assuming that a significant part of the domain consists of non-Xs. This assumption can often be justified as a kind of ceteris paribus principle.
TL;DR: In this article, the role of expectations in non-monotonic reasoning about objects and properties has been investigated in the context of knowledge representation and reasoning under uncertainty, using a conceptual spaces-based analysis.
Abstract: In Gardenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gardenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.
TL;DR: It is argued that Korean speakers’ strong preference for incremental structure building based on the following core phenomena reflect the procedural aspects of linguistic competence, which are difficult to explain within non-procedural grammar formalisms.
Abstract: This paper shows Korean speakers’ strong preference for incremental structure building based on the following core phenomena: (1) left–right asymmetry; (2) pre-verbal structure building and a strong preference for early association. This paper argues that these phenomena reflect the procedural aspects of linguistic competence, which are difficult to explain within non-procedural grammar formalisms. Based on these observations, I argue for the necessity of a grammar formalism that adopts left-to-right incrementality as a core property of the syntactic architecture. In particular, I aim to show the role of (1) constructive particles; (2) prosody; and (3) structural routines in incremental Korean structure building. Though the nature of this discussion is theory-neutral, in order to formalise this idea I will adopt Dynamic Syntax [DS: Kempson et al. (Dynamic syntax: the flow of language understanding, Blackwell, Oxford, 2001); Cann et al. (The dynamics of language. Elsevier, Oxford, 2005)] in this paper.
TL;DR: This paper provides Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3, the expansion of G3 with a dual intuitionistic negation of the type Sylvan defined.
Abstract: The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic B
$$_{\text {M}}$$
with a dual intuitionistic negation of the type Sylvan defined for the extension CC
$$\omega $$
of da Costa’s paraconsistent logic C
$$\omega $$
. We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3
$$_{\text {DH}}$$
, the expansion of G3
$$_{+}$$
with a dual intuitionistic negation of the kind considered by Sylvan (G3
$$_{+}$$
is the positive fragment of Godelian 3-valued logic G3). All logics in the paper are paraconsistent.
TL;DR: This paper presents a novel, Dynamic Syntax-based approach to the phenomenon of differential object marking in Kazakh, which can be extended at least to other Turkic languages displaying this phenomenon.
Abstract: This paper presents a novel, Dynamic Syntax-based approach to the phenomenon of differential object marking in Kazakh, which can be extended at least to other Turkic languages displaying this phenomenon. It is demonstrated that the difference in the pragmatics associated with marked and unmarked direct objects, as well as the syntactic restrictions on the positioning of unmarked direct objects, can be elegantly and succinctly explicated through the application of the notions of fixed and unfixed nodes, without the need for proposing special syntactic positions or additional pragmatics for the accusative case.
TL;DR: In this article, a deontic reinterpretation of dynamic epistemic logic is proposed to formalize legal competences, and in particular for the Hohfeldian categories of power and immunity.
Abstract: We propose a new formalization of legal competences, and in particular for the Hohfeldian categories of power and immunity, through a deontic reinterpretation of dynamic epistemic logic. We argue that this logic explicitly captures the norm-changing character of legal competences while providing a sophisticated reduction of the latter to static normative positions. The logic is completely axiomatizable, and we apply it to a concrete case in German contract law to illustrate that it can capture the distinction between legal ability and legal permissibility.
TL;DR: In this paper, a fragment of relational syllogisms named RELSYLL is presented, consisting of quantified statements with a special set of numerical quantifiers, and introduce a number of concepts that are useful for the later sections.
Abstract: In the first half of this paper, we present a fragment of relational syllogisms named RELSYLL consisting of quantified statements with a special set of numerical quantifiers, and introduce a number of concepts that are useful for the later sections, including indirect reduction, quantifier transformations and equivalence of syllogisms. After determining the valid and invalid syllogisms in RELSYLL, we then introduce two Derivation Methods which can be used to derive valid relational syllogisms based on known valid simple syllogisms. We also show that the two Methods are sound and complete for RELSYLL. In the second half of this paper, we discuss ways to extend the Derivation Methods, including the use of more valid syllogisms and the use of existential assumptions. In this way, we are able to derive more relational syllogisms that contain other types of non-classical quantifiers, including “only” and proportional quantifiers. Finally, we state and prove a proposition concerning the relationship between the two Methods.
TL;DR: A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz's logic Ł3 is defined and several properties of this class and/or some of its subclasses are investigated.
Abstract: The present paper is a sequel to Robles et al. (J Logic Lang Inf 29(3):349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property (vsp) and vsp-related properties.
TL;DR: In this paper, a compositional distributional semantics of Dynamic Syntax (DS) is proposed to enable incremental judgements of similarity needed for the modelling of disambiguation.
Abstract: Despite the incremental nature of Dynamic Syntax (DS), the semantic grounding of it remains that of predicate logic, itself grounded in set theory, so is poorly suited to expressing the rampantly context-relative nature of word meaning, and related phenomena such as incremental judgements of similarity needed for the modelling of disambiguation. Here, we show how DS can be assigned a compositional distributional semantics which enables such judgements and makes it possible to incrementally disambiguate language constructs using vector space semantics. Building on a proposal in our previous work, we implement and evaluate our model on real data, showing that it outperforms a commonly used additive baseline. In conclusion, we argue that these results set the ground for an account of the non-determinism of lexical content, in which the nature of word meaning is its dependence on surrounding context for its construal.
TL;DR: The authors demonstrate that the total negation is actually derived from the interaction between syntax, semantics and pragmatics, rather than being determined by purely syntactic means, in Mandarin Chinese.
Abstract: Minimizers are widely acknowledged cross-linguistically to denote a minimal quantity, extent or degree. With respect to minimizers in Mandarin Chinese, Shyu (Linguistics 54:1355–1395, 2016) claims that their so-called negative polarity is purely syntactically determined and is facilitated by the lian…dou (‘including…all’) EVEN construction. Within the framework of Dynamic Syntax (Kempson et al., Dynamic syntax: the flow of language understanding, Blackwell, 2001; Cann et al., The dynamics of language, Elsevier, 2005) which allows for interaction between syntactic, semantic and pragmatic information, we demonstrate that the total negation is actually derived from the interaction between syntax, semantics and pragmatics, rather than being determined by purely syntactic means.
TL;DR: A new type of rules into Natural Deduction, elimination rules by composition that give a more direct treatment of additive disjunction, multiplicative conjunction, existence quantifier and possibility modality are introduced.
Abstract: The paper introduces a new type of rules into Natural Deduction, elimination rules by composition. Elimination rules by composition replace usual elimination rules in the style of disjunction elimination and give a more direct treatment of additive disjunction, multiplicative conjunction, existence quantifier and possibility modality. Elimination rules by composition have an enormous impact on proof-structures of deductions: they do not produce segments, deduction trees remain binary branching, there is no vacuous discharge, there is only few need of permutations. This new type of rules fits especially to substructural issues, so it is shown for Lambek Calculus, i.e. intuitionistic non-commutative linear logic and to its extensions by structural rules like permutation, weakening and contraction. Natural deduction formulated with elimination rules by composition from a complexity perspective is superior to other calculi.
TL;DR: In this paper, the authors give a formal analysis of the underlying mechanisms for reasoning with ambiguous propositions, both from an algebraic and a logical point of view, and show that sound reasoning with ambiguity requires a distinction between equivalence on the one and congruence in the other side.
Abstract: We treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it is no less obvious that ambiguous propositions entail other propositions (both ambiguous and unambiguous), and are entailed by other propositions. This article gives a formal analysis of the underlying mechanisms, both from an algebraic and a logical point of view. The main result can be summarized as follows: sound (and complete) reasoning with ambiguity requires a distinction between equivalence on the one and congruence on the other side: the fact that $$\alpha $$
entails $$\beta $$
does not imply $$\beta $$
can be substituted for $$\alpha $$
in all contexts preserving truth. Without this distinction, we will always run into paradoxical results. We present the (cut-free) sequent calculus $$\mathsf {AL}^{\textit{cf}}$$
, which we conjecture implements sound and complete propositional reasoning with ambiguity, and provide it with a language-theoretic semantics, where letters represent unambiguous meanings and concatenation represents ambiguity.
TL;DR: In this article, Czelakowski et al. discuss the notion of performability of actions and define a formal ontology based on set-theoretic constructs, which is a solid and non-removable foundation of any rational activity.
Abstract: Action theory may be regarded as a theoretical foundation of AI, because it provides in a logically coherent way the principles of performing actions by agents. But, more importantly, action theory offers a formal ontology mainly based on set-theoretic constructs. This ontology isolates various types of actions as structured entities: atomic, sequential, compound, ordered, situational actions etc., and it is a solid and non-removable foundation of any rational activity. The paper is mainly concerned with a bunch of issues centered around the notion of performability of actions. It seems that the problem of performability of actions, though of basic importance for purely practical applications, has not been investigated in the literature in a systematic way thus far. This work, being a companion to the book as reported (Czelakowski in Freedom and enforcement in action. Elements of formal action theory, Springer 2015), elaborates the theory of performability of actions based on relational models and formal constructs borrowed from formal lingusistics. The discussion of performability of actions is encapsulated in the form of a strict logical system . This system is semantically defined in terms of its intended models in which the role of actions of various types (atomic, sequential and compound ones) is accentuated. Since due to the nature of compound actions the system is not finitary, other semantic variants of are defined. The focus in on the system of performability of finite compound actions. An adequate axiom system for is defined. The strong completeness theorem is the central result. The role of the canonical model in the proof of the completeness theorem is highlighted. The relationship between performability of actions and dynamic logic is also discussed.
TL;DR: It is found that, for Euler and linear diagrams, free rides and observational advantages yielded significant improvements in task performance, and the results suggest that observational advantages better explain the cognitive advantages of diagrams over text.
Abstract: Free rides and observational advantages occur in visualizations when they reveal facts that must be inferred from an alternative representation. Understanding whether these concepts correspond to cognitive advantages is important: do they facilitate information extraction, saving the ‘deductive cost’ of making inferences? This paper presents the first evaluations of free rides and observational advantages in visualizations of sets compared to text. We found that, for Euler and linear diagrams, free rides and observational advantages yielded significant improvements in task performance. For Venn diagrams, whilst their observational advantages yielded significant performance benefits over text, this was not universally true for free rides. The consequences are two-fold: more research is needed to establish when free rides are beneficial, and the results suggest that observational advantages better explain the cognitive advantages of diagrams over text. A take-away message is that visualizations with observational advantages are likely to be cognitively advantageous over competing representations.
TL;DR: In this paper, it was shown that the BAT and CABAT logics are rather complex and they can be characterized by neither finitely many valued deterministic semantics nor possible word semantics including neighbourhood semantics.
Abstract: Recently, in an ongoing debate about informal provability, non-deterministic logics of informal provability BAT and CABAT were developed to model the notion. CABAT logic is defined as an extension of BAT logics and itself does not have independent and decent semantics. The aim of the paper is to show that, semantically speaking, both logics are rather complex and they can be characterized by neither finitely many valued deterministic semantics nor possible word semantics including neighbourhood semantics.