The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.

The aim of this paper is to outline a methodological framework for brand equity planning with structuralist rhetorical semiotics. By drawing on the connectionistconceptual model of the brand generative trajectory of signification it will be displayed in a stepwise fashion how a set of nuclear semes and classemes or anintended semic structure that underlies manifest discursive structures may be projected by its internal stakeholders with view to attaining differential brand associations. The suggested methodological framework focuses on the strength and uniqueness (...) of brand associations as integral aspects of a brand’s equity structure and comprises a set of calculi that aim at addressing from a brand textuality point of view how associations may be systematically linked to their key sources with an emphasis on the ad filmic text. The propounded methodology is exemplified by recourse to a corpus of ad filmic texts from the major brand players in the UK cereals market. The argumentative thrust is intent on demonstrating that structuralist rhetorical semiotics is not only useful for analysing/interpreting brand texts, but, moreover, for constructing and for managing them over time. This demonstration is deployed by adopting a synchronic/diachronic and intra--filmic/inter--filmic approach to the formation of brand associations that make up a projected brand equity structure, in the context of embedded product category dynamics. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In (...) the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in (...) the number of truth values, and it is shown that this bound is tight. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable (...) proof-theoretic properties from its associated labelled calculus. (shrink)

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is (...) translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC (...) frames. (shrink)

ABSTRACT It has become standard to conceive of metalinguistic disagreement as motivated by a form of negotiation, aimed at reaching consensus because of the practical consequences of using a word with one content rather than another. This paper presents an alternative motive for expressing and pursuing metalinguistic disagreement. In using words with given criteria, we betray our location amongst social categories or groups. Because of this, metalinguistic disagreement can be used as a stage upon which to perform a social identity. (...) The ways in which metalinguistic disagreements motivated in this way diverge in character from metalinguistic negotiations are described, as are several consequences of the existence of metalinguistic disagreements motivated in this way. (shrink)

In this essay I give a complete join semi-lattice of possible display-equivalence schemes for Display Logic, using the standard connectives, and leaving fixed only the schemes governing the star. In addition to proving the completeness of this list, I offer a discussion of the basic properties of these schemes.

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated (...) labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp hypotheses were (...) defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

The actual and potential uses of holograms in museum displays, and the philosophy of knowledge and progress that they represent. Magazine journalists, museum curators, and historians sometimes face similar challenges in making topics or technologies relevant to wider audiences. To varying degrees, they must justify the significance of their subjects of study by identifying a newsworthy slant, a pedagogical role, or an analytical purpose. This chasse au trésor may skew historical story telling itself. In science and technology studies, the problem (...) potentially is worst for those subjects that do not retain an enduring capacity for spectacle or do not readily conform to templates of progress or economic importance. The case of holography is an excellent illustration of these points. An unusually wide-ranging subject, holography has attracted competing interpretations of intellectual novelty, technological application, and cultural significance. This paper examines the history of museum collections and exhibits of holography from the explosion of interest in the technique in 1964 to the end of the twentieth century. I argue that holography presents a particular challenge to museum collections and to popular representations of the history of science and technology. (shrink)

Post-Fregean theorists use 'quotation' to denote indifferently both colloquially called quotations (repetitions of prior utterances) and what I call 'displays': 'Rot' means red. Colloquially, quotation is a strictly historical property, not semantic or syntactic. Displays are semantically and syntactically distinctive sentential elements. Most displays are not quotations. Pure echo quotations (Cosmological arguments involve "an unnecessary shuffle") aren't displays. Frege-inspired formal languages stipulate that enquotation forms a singular term referring to the enquoted expression (type). Formalist enquotations differ semantically and syntactically from (...) natural language displays. Call them autonomes, and mark them with stars: *Rot* means red. In formal languages, an unenstarred expression has only one meaning, and an autonome has only one meaning viz., a name (or indexical) designating the unenstarred expression (type). Stars have semantic content and can’t disambiguate. Display punctuation only disambiguates; it says only: This material is displayed. Displays have a semantic function; their marks don't.nDisplays are not terms or lexical items. Displays are objects incorporable into utterances. Such incorporation enables them to be linguistically appropriated much as we appropriate speech-external objects by extrasentential supplementation (e.g., gesturing) to identify the extension of a term by ostending the object -- but now without any extrasentential supplement. Displays are always adjunctive to an (implicit or explicit) ostensionable term, a term whose extension is identifiable by ostending an object. The display-ostensionable term extension relations are various. A display may (1) be the term's referent, or (2) represent the term's extension by (a) replicating or (b) instantiating or (c) expressing the term's referent, or (e) instantiating the property the term predicates. (shrink)

We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.

In his Tractatus, Wittgenstein sets out what he calls his N-operator notation which can be used to calculate whether an expression is a tautology. In his Laws of Form, George Spencer Brown offers what he calls a “primary algebra” for such calculation. Both systems are perplexing. But comparing two blurry images can reduce noise, producing a focus. This paper reveals that Spencer Brown independently rediscovered the quantifier-free part of the N-operator calculus. The comparison sheds a flood light on each and (...) from the letters of correspondence we shall find that Russell, as one might have surmised, was a catalyst for both. (shrink)

Post-Fregean theorists use 'quotation' to denote indifferently both colloquially called quotations (repetitions of prior utterances) and what I call 'displays': 'Rot' means red. Colloquially, quotation is a strictly historical property, not semantic or syntactic. Displays are semantically and syntactically distinctive sentential elements. Most displays are not quotations. Pure echo quotations (Cosmological arguments involve "an unnecessary shuffle") aren't displays. Frege-inspired formal languages stipulate that enquotation forms a singular term referring to the enquoted expression (type). Formalist enquotations differ semantically and syntactically from (...) natural language displays. Call them autonomes, and mark them with stars: *Rot* means red. In formal languages, an unenstarred expression has only one meaning, and an autonome has only one meaning viz., a name (or indexical) designating the unenstarred expression (type). Stars have semantic content and can’t disambiguate. Display punctuation only disambiguates; it says only: This material is displayed. Displays have a semantic function; their marks don't. Displays are not terms or lexical items. Displays are objects incorporable into utterances. Such incorporation enables them to be linguistically appropriated much as we appropriate speech-external objects by extrasentential supplementation (e.g., gesturing) to identify the extension of a term by ostending the object -- but now without any extrasentential supplement. Displays are always adjunctive to an (implicit or explicit) ostensionable term, a term whose extension is identifiable by ostending an object. The display-ostensionable term-extension relations are various. A display may (1) be the term's referent, or (2) represent the term's extension by (a) replicating or (b) instantiating or (c) expressing the term's referent, or (e) instantiating the property the term predicates. (shrink)

Recent advances in our understanding of visual perception have shown it to be a far more complex and counterintuitive process than previously believed. Several important consequences follow from this. First, the design of an effective statistical graphics system is unlikely to succeed based on intuition alone; instead, it must rely on a more sophisticated, systematic approach. The basic elements of such an approach are outlined here, along with several design principles. An overview is then given of recent advances in our (...) understanding of visual perception, including rapid perception, visual attention, and scene perception. It then is argued that the mechanisms involved can be successfully harnessed to allow data to be displayed more effectively than at present. Several directions of development are discussed, including effective use of visual attention, the display of dynamic information, and the effective use of nonattentional and nonconscious perceptual systems. (shrink)

We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the (...) original proof. We then present a linear natural deduction calculus that makes use of formal illocutionary expressions in such a way that unique readability for derivations is guaranteed – thus showing that formalizing illocutionary expressions can eliminate the need for commentary. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)

In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if its (...) translation is a tautology of its corresponding σ-system. We then use these results to obtain other key advantages. Most interestingly, we provide a recipe for building unlabeled sequent calculi for σ-systems. We then exemplify this with a σ-system useful for logics of the ST family, and prove soundness and completeness for it, which indirectly gives us a calculus for the metainferences of all those mixed systems. Finally, we respond to some possible objections and show how our σ-framework can shed light on the “obeying” discussion within mixed metainferential contexts. (shrink)

By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name (...) in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)

This chapter presents an overview of several recent developments in vision science, and outlines some of their implications for the management of visual attention in graphic displays. These include ways of sending attention to the right item at the right time, techniques to improve attentional efficiency, and possibilities for offloading some of the processing typically done by attention onto nonattentional mechanisms. In addition it is argued that such techniques not only allow more effective use to be made of visual attention, (...) but also open up new possibilities for human-machine interaction. (shrink)

The experiments reported herein probe the visual cortical mechanisms that control near–far percepts in response to two-dimensional stimuli. Figural contrast is found to be a principal factor for the emergence of percepts of near versus far in pictorial stimuli, especially when stimulus duration is brief. Pictorial factors such as interposition (Experiment 1) and partial occlusion Experiments 2 and 3) may cooperate, as generally predicted by cue combination models, or compete with contrast factors in the manner predicted by the FACADE model. (...) In particular, if the geometrical conŽ guration of an image favors activation of cortical bipole grouping cells, as at the top of a T-junction, then this advantage can cooperate with the contrast of the conŽ guration to facilitate a near–far percept at a lower contrast than at an X-junction. Varying the exposure duration of the stimuli shows that the more balanced bipole competition in the X-junction case takes longer exposure times to resolve than the bipole competition in the T-junction case (Experiment 3). (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting (...) to embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

Analytic philosophy has been perhaps the most successful philosophical movement of the twentieth century. While there is no one doctrine that defines it, one of the most salient features of analytic philosophy is its reliance on contemporary logic, the logic that had its origin in the works of George Boole and Gottlob Frege and others in the mid‐to‐late nineteenth century. Boolean algebra, the heart of Boole's contributions to logic, has also come to represent a cornerstone of modern computing. Frege had (...) broad philosophical interests, and his writings on the nature of logical form, meaning and truth remain the subject of intense theoretical discussion, especially in the analytic tradition. Frege's works, and the powerful new logical calculi developed at the end of the nineteenth century, influenced many of its most seminal figures, such as Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap. (shrink)

In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...) relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six. (shrink)

This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively(for n=2,...,5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound (...) and complete, and it is shown that the proof search for G3. ST2 is terminating and therefore the logic is decidable. (shrink)

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

People display recognizably characteristic behavioral patterns across time and situations, with a given degree of regularity. These patterns may justify the attribution of personality traits. It is arguably the commonsense view that the proper explanation of these behavioral regularities is given by intrinsic properties of the agent’s psychology. In this paper, I argue for an externalistic view of the causal basis of personality-characteristic behaviors. According to the externalistic view, the relevant behavioral regularities are better understood as the result of (...) a systematic interaction between features internal to the agent and environmental-situational factors. Moreover, if the premise is granted that people are typically able to exercise a certain degree of control over the environmental-situational conditions they find themselves in, the resulting picture is of active sort of externalism, as people may at times engage in selection and manipulation of environmental-situational conditions as a way of managing their own behavioral tendencies. (shrink)

Subjectology (from Latin subject and logos) studies the internal states of living and nonliving systems capable of symbolic representation of any real content, i.e. to display sensory perceptible information and to transform it into world pictures, the elements of which are symbols whose meaning or sense is determined in the context of the symbolic representation. Субъектология (от лат. subject и logos) изучает внутренние состояния живых и неживых систем, способных к символической репрезентации какого–либо реального содержания, т.е. к отображению чувственно воспринимаемой (...) информации и её преобразованию в картины мира, элементами которых являются символы, значение или смысл которых определяется в контексте символического отображения. (shrink)

The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, (...) called the ALL Project (Accelerated Learning of Logic). Following the introduction, the game of VALIDITY is described, first with reference to the propositional calculus, and then in connection with the first-order predicate calculus with identity. Sections in the text are devoted to discussions of the various rules of derivation employed in both calculi. Three appendices follow the main text; these provide a catalogue of sequents and theorems that have been proved for the propositional calculus and for the predicate calculus, and include suggestions for the classroom use of VALIDITY in university-level courses in mathematical logic. (shrink)

It is often observed in metaethics that moral language displays a certain duality in as much as it seems to concern both objective facts in the world and subjective attitudes that move to action. In this paper, I defend The Dual Aspect Account which is intended to capture this duality: A person’s utterance of a sentence according to which φing has a moral characteristic, such as “φing is wrong,” conveys two things: The sentence expresses, in virtue of its conventional meaning, (...) the belief that φing has a moral property, and the utterance of the sentence carries a generalized conversational implicature to the effect that the person in question has an action-guiding attitude in relation to φing. This account has significant advantages over competing views: (i) As it is purely cognitivist, it does not have the difficulties of expressivism and various ecumenical positions. (ii) Yet, in spite of this, it can explain the close, “meaning-like,” connection between moral language and attitudes. (iii) In contrast to other pragmatic accounts, it is compatible with any relevant cognitivist view. (iv) It does not rest on a contentious pragmatic notion, such as conventional implicature. (v) It does not imply that utterances of complex moral sentences, such as conditionals, convey attitudes. In addition, the generalized implicature in question is fully calculable and cancellable. (shrink)

Humans typically display hindsight bias. They are more confident that the evidence available beforehand made some outcome probable when they know the outcome occurred than when they don't. There is broad consensus that hindsight bias is irrational, but this consensus is wrong. Hindsight bias is generally rationally permissible and sometimes rationally required. The fact that a given outcome occurred provides both evidence about what the total evidence available ex ante was, and also evidence about what that evidence supports. Even (...) if you in fact evaluate the ex ante evidence correctly, you should not be certain of this. Then, learning the outcome provides evidence that if you erred, you are more likely to have erred low rather than high in estimating the degree to which the ex ante evidence supported the hypothesis that that outcome would occur. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

This book presents a philosophical conception of logic -- "logical expressivism"-- according to which the role of logic is to make explicit reason relations, which are often neither monotonic nor transitive. It reveals new perspectives on inferential roles, sequent calculi, representation, truthmakers, and many extant logical theories.

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing (...) we search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

The present study collected a larger set of three-dimensional data on human crania from the Kofun period (as well as from previous periods, i.e., the Jomon and Yayoi periods) in the Japanese archipelago (AD 250 to around 700) than previous studies. Three-dimensional geometric morphometrics were employed to investigate human migration patterns in finer-grained phases. These results are consistent with those of previous studies, although some new patterns were discovered. These patterns were interpreted in terms of demic diffusion, archaeological findings, and (...) historical evidence. In particular, the present results suggest the presence of a gradual geological cline throughout the Kofun period, although the middle period did not display such a cline. This discrepancy might reflect social changes in the middle Kofun period, such as the construction of keyhole-shaped mounds in the peripheral regions. The present study implies that a broader investigation with a larger sample of human crania is essential to elucidating macro-level cultural evolutionary processes. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, further reflections (...) on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)

Mobsters and others engaged in risky forms of social coordination and coercion often communicate by saying something that is overtly innocuous but transmits another message ‘off record’. In both ordinary conversation and political discourse, insinuation and other forms of indirection, like joking, offer significant protection from liability. However, they do not confer blanket immunity: speakers can be held to account for an ‘off record’ message, if the only reasonable interpreta- tions of their utterance involve a commitment to it. Legal liability (...) for speech in the service of criminal behavior displays a similar profile of significant protection from indirection along with potential liability for reasonable interpretations. Specifically, in both ordinary and legal contexts, liability depends on how a reasonable speaker would expect a reasonable hearer to interpret their utterance in the context of utter- ance, rather than on the actual speaker’s claimed communicative intentions. (shrink)

Slurring expressions display puzzling behaviour when embedded, such as under negation and in attitude and speech reports. They frequently appear to retain their characteristic qualities, like offensiveness and propensity to derogate. Yet it is sometimes possible to understand them as lacking these qualities. A theory of slurring expressions should explain this variability. We develop an explanation that deploys the linguistic notion of focus. Our proposal is that a speaker can conversationally implicate metalinguistic claims about the aptness of a focused (...) slurring expression. This explanation of variability relies on independently motivated mechanisms and is compatible with any theory of slurring expressions. (shrink)

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in (...) terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)

Arguably the most foundational principle in perception research is that our experience of the world goes beyond the retinal image; we perceive the distal environment itself, not the proximal stimulation it causes. Shape may be the paradigm case of such “unconscious inference”: When a coin is rotated in depth, we infer the circular object it truly is, discarding the perspectival ellipse projected on our eyes. But is this really the fate of such perspectival shapes? Or does a tilted coin retain (...) an elliptical appearance even when we know it’s circular? This question has generated heated debate from Locke and Hume to the present; but whereas extant arguments rely primarily on introspection, this problem is also open to empirical test. If tilted coins bear a representational similarity to elliptical objects, then a circular coin should, when rotated, impair search for a distal ellipse. Here, nine experiments demonstrate that this is so, suggesting that perspectival shapes persist in the mind far longer than traditionally assumed. Subjects saw search arrays of three-dimensional “coins,” and simply had to locate a distally elliptical coin. Surprisingly, rotated circular coins slowed search for elliptical targets, even when subjects clearly knew the rotated coins were circular. This pattern arose with static and dynamic cues, couldn’t be explained by strategic responding or unfamiliarity, generalized across shape classes, and occurred even with sustained viewing. Finally, these effects extended beyond artificial displays to real-world objects viewed in naturalistic, full-cue conditions. We conclude that objects have a remarkably persistent dual character: their objective shape “out there,” and their perspectival shape “from here.”. (shrink)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly (...) incorporates the semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...) these systems derivability can be characterized in terms of a notion we call absolute global validity. However, arriving at these results doesn’t lead us to disregard local validity. First, because we discuss the conditions under which local, and also global validity, can be expected to coincide with derivability. Secondly, because we show how taking into account certain families of valuations can be useful to describe derivability for different calculi used to present _S__T_ and _T__S_. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...) values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent (...) class='Hi'>calculi for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)

Present-bias is the preference, all else being equal, for positive events to be located in the present rather than the non-present, and for negative events to be located in the non-present rather than the present. Very little attention has been given to present-bias in the contemporary literature on time biases. This may be because it is often assumed that present-bias is not a distinctive psychological kind; that what explains people’s being present-biased is just what explains them displaying various other time-biases. (...) According to this view, there is no need to investigate present-bias independently of investigating these other biases, since present-bias is really just a manifestation of these other biases. We call this the manifestation thesis. We take up the question of whether the manifestation thesis is true, and argue that it is not. Thus, by failing to investigate present-bias in its own right we are failing fully to understand the spectrum of ways in which people display time biases. In turn, we suggest, this may have implications for the ways we evaluate whether present-bias is rationally permissible. (shrink)

In Tulving’s initial characterization, episodic memory was one of multiple memory systems. It was postulated, in pursuit of explanatory depth, as displaying proprietary operations, representations, and substrates such as to explain a range of cognitive, behavioural, and experiential phenomena. Yet the subsequent development of this research program has, paradoxically, introduced surprising doubts about the nature, and indeed existence, of episodic memory. On dominant versions of the ‘common system’ view, on which a single simulation system underlies both remembering and imagining, there (...) are no processes unique to memory to support robust generalizations with inductive potential. Eliminativism about episodic memory seems to follow from the claim that it has no dedicated neurocognitive system of its own. After identifying this under-noticed threat, we push back against modern eliminativists by surveying recent evidence that still indicates specialized mechanisms, computations, and representations that are distinctly mnemic in character. We argue that contemporary realists about episodic memory can retain lessons of the common system approach while resisting the further move to eliminativism. (shrink)