The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So, a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in the spirit of van Benthem's correspondence theory) of arbitrary and ~-elementary classes of frames in this base and in (...) some of its extensions, e.g., £(R,-R,R-1 ,_R-1), £(R,-R,=I=) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced. (shrink)

We present the propositional logic LEC for the two epistemic modalities of current and stable knowledge used by an agent who system-atically enriches his language. A change in the linguistic resources of an agent as a result of certain cognitive processes is something that commonly happens. Our system is based on the logic LC intended to formalize the idea that the occurrence of changes induces the passage of time. Here, the primitive operator C read as: it changes that, defines (...) the temporal succession of states of the world. The notion of current knowledge concerns variable components of the world and it may change over time. We represent it by the primitive operator k read as: the agent currently knows that, and assume that it has S5 properties. The second type of knowledge, symbolized by the primitive operator K read as: the agent stably knows that, relates to constant components of the world and it does not change. As a result of the axiomatic entanglement of C, K and k we show that stable knowledge satisfies axioms of S4.3. K and k modalities are not mutually definable, stable knowledge implies the current one and if the latter never changes, then it comes to be stable. The combination of K and k with the idea of an expanding language allows questioning of the so-called perfect recall principle. It cannot be maintained for both types of knowledge just because of changes in the vocabulary of the agent and possibly the growing spectrum of possible states of the world. We interpret LEC in the semantics of histories of epistemic changes and show that it is complete. Finally, we compare our logic with selected epistemic logics based on the concept of linear discrete time. (shrink)

This article discusses some of the ways in which natural language can express modal information – information which is, to a first approximation, about what could be or must be the case, as opposed to being about what actually is the case. It motivates, explains, and raises problems for Angelika Kratzer's influential theory of modal auxiliaries, and introduces a new approach to one important debate about the relationships between modality, evidentiality, context change, and imperative force.

In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.

What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover, its own internal finite variable hierarchy turns out to work well. Finally, we shall make another move. The above analogy works both ways. Modal operators are like quantifiers, but quantifiers are also like modal operators. This observation inspires a generalized semantics for first-order predicate logic with accessibility constraints on available assignments (cf. N´emeti 1986, 1992) which moves the earlier quantifier restrictions into the semantics. This provides a fresh look at the landscape of possible predicate logics, including candidates sharing various desirable features with basic modal logic – in particular, its decidability. (shrink)

Early modern humans developed mental capabilities that were immeasurably greater than those of nonhuman primates. We see this in the rapid innovation in tool making, the development of complex language, and the creation of sophisticated art forms, none of which we find in our closest relatives. While we can readily observe the results of this high-order cognitive capacity, it is difficult to see how it could have developed. We take up the topic of cave art and archeoacoustics, particularly the (...) discovery that cave art is often closely connected to the acoustic properties of the cave chambers in which it is found. Apparently, early modern humans were able to detect the way sound reverberated in these chambers, and they painted artwork on surfaces that were acoustic “hot spots,” i.e., suitable for generating echoes. We argue that cave art is a form of cross-modality information transfer, in which acoustic signals are transformed into symbolic visual representations. This form of information transfer across modalities is an instance of how the symbolic mind of early modern humans was taking shape into concrete, externalized language. We also suggest that the earliest rock art found in Africa may constitute one of the first fossilized proxies for the expression of full-fledged human linguistic behavior. (shrink)

In the present study, cross-modal (i.e., across sensory modalities such as smell and sound) iconicity (i.e., resemblance) and indexicality (i.e., contiguity) in lexical sensory and emotional signs in Finnish Sign Language will be considered from an articulatory perspective (i.e., the production of signs). Such cross-modal iconicity has not been extensively studied previously, so here, with the help of cognitive semiotics, I aim to carefully describe the cross-modal patterns observed across 118 signs, including 60 sensory signs and 58 emotional signs. (...) The analysis is framed within the theoretical model of Semiotic Hierarchy, which entails a non-reductionist view of meaning. In addition, a pheno-methodological triangulation will be applied: phenomenology (first-person method), literature of phenomenological and semiotic descriptions (second-person perspective) and experimental findings (third-person perspective). The results of this analysis show that (a) 71 of the 118 sensory and emotional signs are cross-modally indexical, (b) only 10 of the 71 signs can be regarded as cross-modally iconic, (c) cross-modal iconicity is highly diagrammatic, (d) iconicity and indexicality are highly integrated, and (e) articulatory feedback matters in the formation of semiotic patterns. This study contributes to our understanding of cross-modal iconicity in signed languages, as well as studies in semiotic systems more generally. (shrink)

Description: The book points to a new logic of singular designators based upon a close analysis of work in the area by contemporary philosophers of language. The philosophers range from Frege, Russell, Quine, Strawson and Dummett to Kripke, Hintikka, Plantinga, Kaplan, Donnellan, Searle and Burge. It is generally taken for granted that proper names are rigid designators, having no meaning content, which explains their intranslatability into other languages. However, they do have their modes of presentation that must constitute their (...) sense. There is little room for contradiction here in admitting that proper names have a sense, which does not amount to meaning. One of the advantages of this position is that it blocks the emergence of the Kripkean puzzle about belief by accepting different belief contents corresponding to a variation in the senses of the names involved. Is Kripke's distinction between rigid and non-rigid designators finally valid' the author asks, questioning the corollaries that are supposed to follow from the distinction, viz., that proper names do not have descriptive backing, and that there are contingent a priori truths. He draws our attention to predicative occurrences of proper names, in the modal context, matching corresponding occurrences of definite descriptions. His explanation of contingency, where proper names or definite descriptions are involved, is innovatively straight, simple and broad-based, at par with situations having ordinary predicates. Parts of the book have taken a final shape in response to comments by Strawson, Dummett and Burge. (shrink)

Natural languages come in two different modalities. The impact of modality on the grammatical structure and linguistic theory has been discussed at great length in the last 20 years. By contrast, the impact of modality on linguistic data elicitation and collection, corpus studies and experimental (psycholinguistic) studies is still underinvestigated (van Herreweghe/Vermeerbergen 2012; Orfanidou et al. 2015). In this paper, we address specific challenges that arise in judgement data elicitation and experimental studies of sign languages. These challenges are related to (...) the socio-linguistic status of the Deaf community and the larger variability across signers within the same community, to the social status of sign languages, to properties of ;he visual-gestural modality and its interface with gesture, to methodological aspects of handling sign language data, and to specific linguistic features of sign languages. While some of these challenges also pertain to (some varieties of) spoken languages, other challenges are more modality-specific. In addition, the special combination of the challenges discussed in this paper seems to be a specific facet empirical research on sign languages is faced with. In addition, we discuss the complementarity of theoretical approaches and experimental studies and show how the interaction of both approaches contributes to a better understanding of sign languages in particular and linguistic structures in general. (shrink)

The contract review process can be a costly and time-consuming task for lawyers and clients alike, requiring significant effort to identify and evaluate the legal implications of individual clauses. To address this challenge, we propose the use of natural language processing techniques, specifically text classification based on deontic tags, to streamline the process. Our research question is whether natural language processing techniques, specifically dense vector embeddings, can help semi-automate the contract review process and reduce time and costs for (...) legal professionals reviewing deontic modalities in contracts. In this study, we create a domain-specific dataset and train both baseline and neural network models for contract sentence classification. This approach offers a more efficient and cost-effective solution for contract review, mimicking the work of a lawyer. Our approach achieves an accuracy of 0.90, showcasing its effectiveness in identifying and evaluating individual contract sentences. (shrink)

All languages, both spoken and signed, make a formal distinction between two types of terms in a proposition – terms that identify what is to be talked about (nominals) and terms that say something about this topic (predicates). Here we explore conditions that could lead to this property by charting its development in a newly emerging language – Nicaraguan Sign Language (NSL). We examine how handshape is used in nominals vs. predicates in three Nicaraguan groups: (1) homesigners who (...) are not part of the Deaf com- munity and use their own gestures, called homesigns, to communicate; (2) NSL cohort 1 signers who fashioned the first stage of NSL; (3) NSL cohort 2 signers who learned NSL from cohort 1. We compare these three groups to a fourth: (4) native signers of American Sign Language (ASL), an established sign language. We focus on handshape in predicates that are part of a productive classifier system in ASL; handshape in these predicates varies sys- tematically across agent vs. no-agent contexts, unlike handshape in the nominals we study, which does not vary across these contexts. We found that all four groups, including home- signers, used handshape differently in nominals vs. predicates – they displayed variability in handshape form across agent vs. no-agent contexts in predicates, but not in nominals. Variability thus differed in predicates and nominals: (1) In predicates, the variability across grammatical contexts (agent vs. no-agent) was systematic in all four groups, suggesting that handshape functioned as a productive morphological marker on predicate signs, even in homesign. This grammatical use of handshape can thus appear in the earliest stages of an emerging language. (2) In nominals, there was no variability across grammatical con- texts (agent vs. no-agent), but there was variability within- and across-individuals in the handshape used in the nominal for a particular object. This variability was striking in homesigners (an individual homesigner did not necessarily use the same handshape in every nominal he produced for a particular object), but decreased in the first cohort of NSL and remained relatively constant in the second cohort. Stability in the lexical use of handshape in nominals thus does not seem to emerge unless there is pressure from a peer linguistic community. Taken together, our findings argue that a community of users is essential to arrive at a stable nominal lexicon, but not to establish a productive morpholog- ical marker in predicates. Examining the steps a manual communication system takes as it moves toward becoming a fully-fledged language offers a unique window onto factors that have made human language what it is. (shrink)

The subject of my article is the principle of characterization – the most controversial principle of Meinong’s Theory of Objects. The aim of this text is twofold. First of all, I would like to show that Russell’s well-known objection to Meinong’s Theory of Objects can be reformulated against a new modal interpretation of Meinongianism that is presented mostly by Graham Priest. Secondly, I would like to propose a strategy which gives uncontroversial restriction to the principle of characterization and which allows (...) to avoid Russell’s argument. The strategy is based on the distinction between object- and metalanguage, and it applies to modal Meinongianism as well as to other so-called Meinongian theories. (shrink)

Modality is a category of linguistic meaning having to do with the expression of possibility and necessity. A modalized sentence locates an underlying or prejacent proposition in the space of possibilities. Sandy might be home says that there is a possibility that Sandy is home. Sandy must be home says that in all possibilities, Sandy is home. The counterpart of modality in the temporal domain should be called “temporality”, but it is more common to talk of tense and aspect, the (...) prototypical verbal expressions of temporality. Together, modality and temporality are at the heart of the property of “displacement” that enables natural language to talk about affairs beyond the actual here and now. (shrink)

Cohen (2023) takes a fair and measured approach to the question of what ChatGPT means for bioethics. The hype cycles around AI often obscure the fact that ethicists have developed robust frameworks...

The set of English modal verbs is widely recognised to communicate two broad clusters of meanings: epistemic and root modal meanings. A number of researchers have claimed that root meanings are acquired earlier than epistemic ones; this claim has subsequently been employed in the linguistics literature as an argument for the position that English modal verbs are polysemous (Sweetser 1990). In this paper I offer an alternative explanation for the later emergence of epistemic interpretations by liniking them to the development (...) of the child's theory of mind (Wellman 1990). If correct, this hypothesis might have important implications for the shape of the semantics of modal verbs. (shrink)

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of their semantics. This paper (...) is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

It is widely assumed in the developmental literature that certain classes of modal expression appear later in language acquisition than others; specifically, epistemic interpretations lag behind non-epistemic interpretations. An explanation for these findings is proposed in terms of the child’s developing theory of mind, i.e. the ability to attribute to oneself and others mental representations, and to reason inferentially about them. It is hypothesized that epistemic modality crucially implicates theory-of-mind abilities and is therefore expected to depend on prior developments (...) in the child's ability to handle representations of mental representations. In support of this hypothesis, it is shown that autistic individuals have difficulty with epistemics. (shrink)

This book is a collection of papers on modals in the languages of Europe, written by experts in the area of modality. It provides readers with a wealth of data and addresses the issues of under which circumstances modals are borrowed, from which linguistic materials they typically arise in these languages, and whether and how modals form a system which is separate from other word classes.

Norris presents a series of closely linked chapters on recent developments in epistemology, philosophy of language, cognitive science, literary theory, musicology and other related fields. While to this extent adopting an interdisciplinary approach, Norris also very forcefully challenges the view that the academic "disciplines" as we know them are so many artificial constructs of recent date and with no further role than to prop up existing divisions of intellectual labour. He makes his case through some exceptionally acute revisionist readings (...) of diverse thinkers such as Derrida, Paul de Man, Wittgenstein, Chomsky, Michael Dummett and John McDowell. In each instance Norris stresses the value of bringing various trans-disciplinary perspectives to bear while none-the-less maintaining adequate standards of area-specific relevance and method. Most importantly he asserts the central role of recent developments in cognitive science as pointing a way beyond certain otherwise intractable problems in philosophy of mind and language. (shrink)

The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I (...) think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity. (shrink)

Sign language interpreting is a cognitively challenging task performed mostly by second language learners. SLI students must first gain language fluency in a new visuospatial modality and then move between spoken and signed modalities as they interpret. As a result, many students plateau before reaching working fluency, and SLI training program drop-out rates are high. However, we know little about the requisite skills to become a successful interpreter: the few existing studies investigating SLI aptitude in terms of (...) linguistic and cognitive skills lack baseline measures. Here we report a 3-year exploratory longitudinal skills assessments study with British Sign Language -English SLI students at two universities. Our aims were two-fold: first, to better understand the prerequisite skills that lead to successful SLI outcomes; second, to better understand how signing and interpreting skills impact other aspects of cognition. A battery of tasks was completed at four time points to assess skills, including but not limited to: multimodal and unimodal working memory, 2-dimensional and 3-dimensional mental rotation, and English comprehension. Dependent measures were BSL and SLI course grades, BSL reproduction tests, and consecutive SLI tasks. Results reveal that initial BSL proficiency and 2D-MR were associated with selection for the degree program, while visuospatial working memory was linked to continuing with the program. 3D-MR improved throughout the degree, alongside some limited gains in auditory, visuospatial, and multimodal working memory tasks. Visuospatial working memory and MR were the skills closest associated with BSL and SLI outcomes, particularly those tasks involving sign language production, thus, highlighting the importance of cognition related to the visuospatial modality. These preliminary data will inform SLI training programs, from applicant selection to curriculum design. (shrink)

The reasoning abilities of large language models (LLMs) are the topic of a growing body of research in artificial intelligence and cognitive science. In this paper, we probe the extent to which a dozen LLMs are able to distinguish logically correct inferences from logically fallacious ones. We focus on inference patterns involving conditionals (e.g., 'If Ann has a queen, then Bob has a jack') and epistemic modals (e.g., 'Ann might have an ace', 'Bob must have a king'). These inference (...) patterns have been of special interest to logicians, philosophers, and linguists, since they plausibly play a central role in human reasoning. Assessing LLMs on these inference patterns is thus highly relevant to the question of how much the reasoning abilities of LLMs match those of humans. Among the LLMs we tested, all but GPT-4 often make basic mistakes with conditionals. Moreover, even GPT-4 displays logically inconsistent judgments across inference patterns involving epistemic modals. (shrink)

With the aim of providing an empiricist-friendly rational reconstruction of scientists’ modal talk, I represent and defend the following unoriginal idea of relative modalities, focused on natural ones: the assertion of physical necessity of φ can be understood as the logical provability of φ from the background theory of the context of assertion. I elaborate on my conception of the background theory, and reply to a number of objections, among which an objection concerning the failure of factivity.

The academic review of the book “On Bulgarian Philosophical Culture” by Atanas Stamatov deals with the main areas and problems explored by the author. The book consists of various articles written by Atanas Stamatov over the past 30 years and the review evaluates their importance and significance. The text examines in detail the methods and main accents in Stamatov's works – the concept of “Bulgarian philosophical culture”, the philosophical concepts in the Old Bulgarian language, the philosophy (...) education, philosophy of history in Bulgaria, as well as the analysis of the key thinkers in the Bulgarian tradition. (shrink)

Griffiths and Machery (2008) argue that innateness is a ?folk biological? notion, which, as such, has no useful reconstruction in contemporary biology. If this is so, not only is it wrong to identify the vernacular notion with the precise theoretical concept of canalization, but worse, it would appear that many of the putative scientific claims for particular competences and capacities being innate are simply misplaced. The present paper challenges the core substantive claim of Griffiths and Machery's position, namely, that innateness (...) understood on canalization lines as environment-independent development (somehow and to some degree) is a confused, outmoded notion. It will be contended that the modality-independence of language offers a prima facie case against Griffiths and Machery's general position. (shrink)

Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language ℒ' is the least expressive extension of ℒ with interpolation. For instance, let ℳ be the extension of the basic modal language with a difference operator [7]. First-order logic is the least expressive extension of ℳ with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment.

In recent work, Amie Thomasson has defended what she calls normativism about metaphysical modality. She claims that discourse about metaphysical modality primarily serves a non-descriptive function, and builds a theory of such discourse around this claim. In this text, I critically discuss Thomasson’s view. Chief among the problems I go on to discuss is that Thomasson’s account of the meanings of modal expressions does not solve the problems she intends it to solve (among them solving the Frege-Geach problem), that there (...) is no significant ordinary practice of making metaphysically modal claims in the first place, and that the general problem she identifies and seeks to solve goes beyond discourse about metaphysical modality so a theory focused on metaphysical modal discourse is not general enough to deal with the problem. (shrink)

Cognitive Science, Volume 46, Issue 6, June 2022.

Gaze behavior is an important component of children’s language, cognitive, and sociocultural development. This is especially true for young deaf children acquiring a signed language—if they are not looking at the language model, they are not getting linguistic input. Deaf caregivers engage their deaf infants and toddlers using visual and tactile strategies to draw in, support, and promote their child’s visual attention; we argue that these caregiver actions create a developmental niche that establishes the visual modality capital (...) their child needs for successful sign language learning. But most deaf children do not have deaf signing parents and they will need to rely on adult signing teachers if they are to acquire a signed language at an early age. This study examines classroom interactions between a Deaf teacher, her teacher’s aide, and six deaf preschoolers to document the teachers’ “everyday practices” as they socialize the gaze behavior of these children. Utilizing a detailed behavioral and linguistic analysis of two video-recorded book-sharing contexts, we present data summarizing the teacher’s attention-getting actions directed toward the children and the discourse-embedded cues that signal the teacher’s expectations for student participation in the signed conversation. We observed that the teacher’s behaviors differed according to the parent status of the deaf preschooler suggesting that Deaf children of Deaf parents arrive to the preschool classroom with well-developed self-regulation of their attention or gaze. The teachers also used more physical and explicit cueing with the deaf children of hearing parents—possibly to promote their ability to leverage the visual modality for sign language acquisition. We situate these socialization patterns within a framework that integrates notions of intuitive or indigenous practices, developmental niche, and modality capital. Implications for early childhood deaf education are also discussed. (shrink)

In order to avoid the use of individual variables in predicate calculus, several authors proposed language whose expressions can be interpreted, in general, as denotations of predicates . The present author also proposed a language of this kind [5]. The absence of individual variables makes all these languages rather different from the traditional language of predicate calculus and from the usual language of mathematics. The translation procedures from the ordinary predicate languages into the predicate languages without (...) individual variables and vice versa have a technical character. It is desirable to make possible carrying out such procedures by performing some transformations in a suitable new language which comprises both a sublanguage similar to the ordinary predicate languages and another one not using individual variables. We shall propose now a language of the desired kind. The expressions of this language could be interpreted, in general, as denoting predicates which depend on parameters on a given object domain – this predicate has one argument and depends on one parameter). The proposed language will have the modal features noted in [3] and [5]. It is worthy of mention that the language proposed at the end of [4] although containing expressions interpreted as predicates and expressions with parameters does not allow simultaneous availability of argument places and parameters. (shrink)

Does general validity or real world validity better represent the intuitive notion of logical truth for sentential modal languages with an actuality connective? In (Philosophical Studies 130:436–459, 2006) I argued in favor of general validity, and I criticized the arguments of Zalta (Journal of Philosophy 85:57–74, 1988) for real world validity. But in Nelson and Zalta (Philosophical Studies 157:153–162, 2012) Michael Nelson and Edward Zalta criticize my arguments and claim to have established the superiority of real world validity. Section 1 (...) of the present paper introduces the problem and sets out the basic issues. In Sect. 2 I consider three of Nelson and Zalta’s arguments and find all of them deficient. In Sect. 3 I note that Nelson and Zalta direct much of their criticism at a phrase (‘true at a world from the point of view of some distinct world as actual’) I used only inessentially in Hanson (Philosophical Studies 130:436–459, 2006), and that their account of the philosophical foundations of modal semantics leaves them ill equipped to account for the plausibility of modal logics weaker than S5. Along the way I make several general suggestions for ways in which philosophical discussions of logical matters–especially, but not limited to, discussions of truth and logical truth for languages containing modal and indexical terms–might be facilitated and made more productive. (shrink)

We propose a generalization of Sahlqvist formulas to polyadic modal languages by representing such languages in a combinatorial PDL style and thus, in particular, developing what we believe to be the right syntactic approach to Sahlqvist formulas at all. The class of polyadic Sahlqvist formulas PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

A system of modal logic with the operator is proposed, and proved complete. In contrast with a previous one by Stalnaker and Thomason, this system does not require two categories of singular terms.