It is difficult to create spoken forms that can be understood on the spot. But the manual modality, in large part because of its iconic potential, allows us to construct forms that are immediately understood, thus requiring essentially no time to develop. This paper contrasts manual forms for actions produced over three time spans—by silent gesturers who are asked to invent gestures on the spot; by homesigners who have created gesture systems over their life spans; and by (...) signers who have learned a conventional sign language from other signers—and finds that properties of the predicate differ across these time spans. Silent gesturers use location to establish co-reference in the way established sign languages do, but they show little evidence of the segmentation sign languages display in motion forms for manner and path, and little evidence of the finger complexity sign languages display in handshapes in predicates representing events. Homesigners, in contrast, not only use location to establish co-reference but also display segmentation in their motion forms for manner and path and finger complexity in their object handshapes, although they have not yet decreased finger complexity to the levels found in sign languages in their handling handshapes. The manual modality thus allows us to watch language as it grows, offering insight into factors that may have shaped and may continue to shape human language. (shrink)

Sign languages modulate the production of signs in space and use this spatial modulation to refer back to entities—to maintain coreference. We ask here whether spatial modulation is so fundamental to language in the manual modality that it will be invented by individuals asked to create gestures on the spot. English speakers were asked to describe vignettes under 2 conditions: using gesture without speech, and using speech with spontaneous gestures. When using gesture alone, adults placed gestures for particular (...) entities in non-neutral locations and then used those locations to refer back to the entities. When using gesture plus speech, adults also produced gestures in non-neutral locations but used the locations coreferentially far less often. When gesture is forced to take on the full burden of communication, it exploits space for coreference. Coreference thus appears to be a resilient property of language, likely to emerge in communication systems no matter how simple. (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)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 210 Seiten: 75-104.

Intensional logic is the technical study of such intensional phenomena in human reasoning as modality, knowledge, or flow of time. These all require a richer semantic picture than standard truth values in one static environment. Such a picture is provided by so-called possible worlds semantics, a paradigm which is surveyed in this book, both as to its external sources of motivation and as to the internal dynamics of the resulting program. In particular, Manual of Intensional Logic presents the (...) major classical topics, including modal logic, tense logic, and conditional logic, all of which illustrate motivations coming from philosophy and linguistics. The Book also discusses recent computational applications in computer science and AI. Finally, Manual of Intensional Logic takes up recent developments in the study of language and information making themselves felt in the area. The Book examines the role of partial information--with illustrations drawn from different branches of Intensional Logic--and various influences stemming from current theories of the semantics of natural language, involving generalized quantifiers and theories of types. (shrink)

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could (...) have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator. (shrink)

This paper presents a study of modality in Iranian Sign Language (ZEI) from a cognitive perspective, aimed at analyzing two linguistic channels: facial and manual. While facial markers and their grammatical functions have been studied in some sign languages, we have few detailed analyses of the facial channel in comparison with the manual channel in conveying modal concepts. This study focuses on the interaction between manual and facial markers. A description of manual modal signs is (...) offered. Three facial markers and their modality values are also examined: squinted eyes, brow furrow, and downward movement of lip corners (horseshoe mouth). In addition to offering this first descriptive analysis of modality in ZEI, this paper also applies the Cognitive Grammar model of modality, the Control Cycle, and the Reality Model, classifying modals into two kinds, effective and epistemic. It is suggested that effective control, including effective modality, tends to be expressed on the hands, while facial markers play an important role in marking epistemic assessment, one manifestation of which is epistemic modality. ZEI, like some other sign languages, exhibits an asymmetry between the number of manual signs and facial markers expressing epistemic modality: while the face can be active in the expression of effective modality, it is commonly the only means of expressing epistemic modality. By positing an epistemic core in effective modality, Cognitive Grammar provides a theoretical basis for these findings. (shrink)

Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any three-valued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In general, our Translation Manual gives rise to translations that are exponentially longer than their originals. This fact raises the question whether (...) there are three-valued logics for which there is a shorter translation into S5. The answer is affirmative: we present an elegant linear translation of the Logic of Paradox and of Strong Three-valued Logic into S5. (shrink)

Motor inhibitory control, the ability to suppress unwanted actions, has been previously shown to rely on domain-general IC processes that are involved in a wide range of IC tasks. Nevertheless, the existence of effector-specific regions and activation patterns that would differentiate manual vs. oculomotor response inhibition remains unknown. In this study, we investigated the brain dynamics supporting these two response effectors with the same IC task paradigm. We examined the behavioral performance and electrophysiological activity in a group of healthy (...) young people with a Go/NoGo task using the index finger for the manual modality and the eyes for the oculomotor modality. By computing topographic analysis of variance, we found significant differences between topographies of scalp recorded potentials of the two response effectors between 250 and 325 ms post-stimulus onset. The source estimations localized this effect within the left precuneus, a part of the superior parietal lobule, showing stronger activity in the oculomotor modality than in the manual modality. Behaviorally, we found a significant positive correlation in response time between the two modalities. Our collective results revealed that while domain-general IC processes would be engaged across different response effectors in the same IC task, effector-specific activation patterns exist. In this case, the stronger activation of the left precuneus likely accounts for the increased demand for visual attentional processes in the oculomotor Go/NoGo task. (shrink)

The history of contemporary modal logic dates back to the writings of C. S. Lewis in the early part of this century. Since then, a growing body of literature has attested to professional interest in the area, and in a number of related issues in philosophical logic which have received wide attention. The recent development of powerful formal techniques for modal system building, together with an increasing interest in modal logic as a tool for philosophical analysis, have created a need (...) for an up-to-date text to introduce students to this material. Snyder's book attempts to answer this need. Assuming an understanding of elementary propositional logic, Snyder introduces a reductive technique called cancellation for detecting the theorems of a system of logic. This technique, analogous to the construction of Smullyan trees but more compact, is extended to modal and quantified contexts. Cancellation versions of the systems M and Mn of G. H. von Wright, and S4 and S5 of Lewis are developed. Snyder uses a Hintikka type of semantics, showing how the various formal systems are differentiated at the semantic level by differing conditions which must be imposed on the model systems used as interpretations for them. These model systems, and the conditions imposed upon them, are in turn described by means of a metalanguage which is essentially first-order quantificational logic. The power of this technique stems from the fact that for every object language formula of a system, there is a corresponding formula in the metalanguage which describes the conditions an interpretation must meet in order to satisfy the original formula. The conditions that the interpretations of a given system of logic must meet are reflected in this metalanguage as "antecedent assumptions," and these in turn correspond to cancellation rules for the object language. This correspondence is constructed in such a way that the metalinguistic counterpart of each theorem of the system will be a theorem of first-order logic. Snyder's primary interest is in showing how modal logic can be used, with the help of these techniques, to build a large variety of formal systems and to "tailor" such systems to meet a variety of analytical tasks. Simple modal systems are developed for the articulation of a number of modal concepts, in addition to the classic alethic ones. Examples are taken from temporal, deontic, and epistemic logic to show how specific interpretations of the meanings of the relevant operators lead to the incorporation of appropriate conditions in the formal systems used to articulate them. An entire chapter is devoted to a discussion of the paradoxes of material and strict implication, and to an attempt to articulate the notion of entailment through the development of formal systems which include a dyadic modal operator that is free of these paradoxes. The final chapter discusses such classical issues as proper names, reference, fictional entities, definite descriptions, and existence presuppositions. Appendices deal with such matters as the equivalence of the cancellation systems to more classical axiomatic-deduction systems, and the sketch of a proof of soundness and completeness for all the modal systems presented. While designed as a text, this volume should be of interest to both logicians and those working in metaphysics and language analysis, since the primary concern of the author is to develop techniques that will facilitate the usefulness of modal logic as a tool for philosophical analysis. The instructor's manual contains many suggestions derived from the author's experience in teaching this non-standard treatment of the subject.--K. T. (shrink)

LetA be a quasi-manual with finite operations. Associate to each E = {e 1 ,..., en} εA the set ΓE of modal formulas: □(e 1 ⋁ ··· ⋁ en), ◊ei → ∼□(e 1 ⋁ ··· ⋁ ei−1 ⋁ ei+1 ⋁ ··· ⋁ en), i=1,..., n. Set Γ A = ώ{ΓE|E εA}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of Γ A where the supports are given by {x ε |A ‖ ◊ x is (...) true}. (shrink)

Following a proposal by Kooi and Tamminga, we introduce a conservative translation manual for every four-valued truth-functional propositional logic into a modal logic. However, the application of this translation does not preserve the intuitive reading of the truth-values for every four-valued logic. In order to solve this problem, we modify the translation manual and prove its conservativity by exploiting the method of generalized truth-values.

This paper examines the role of modality resources (e.g., “may”, “often”) in the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) in representing behavioral pathology focusing, in particular, on Attention Deficit Hyperactivity Disorder (ADHD). ADHD diagnosis requires reports of non-practitioners (e.g., carers and teachers); an effective understanding of behavioral descriptors by the lay community is thus of paramount importance. The study combines qualitative linguistic discourse analysis and a corpus approach to study the presence and functions of modality, (...) adopting a Systemic Functional perspective towards language. The study argues that in the DSM-5 modality is an important linguistic resource for conveying clinical significance, inferred from graduations of recurrence and probability. However, adopting features of professional discourse in representing behavioral pathology for non-experts, especially when those resources are inherently evaluative, stresses the need of health literacy among the lay social community and accessibility in health communication materials, particularly when non-practitioners are involved in the diagnosis practice. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

Partindo do conto «O alienista » de Machado de Assis, procuro tecer algumas consideraçāes sobre o 'normal' e o 'patológico' com refêrncia a Georges Canguilhem e à sua obra O normal e o patológico: ao procurar compreender o modo como a medicina estabelece o conceito de 'normal' e, em oposiçãāo, o de 'patológico', o seu pensamento foi influenciando um leque alargado de saberes que vāo desde a compreensāo da individualidade e a valonzaçāo da normatividade até ao conjunto das questōes relativas (...) ao trìnómio ética-política-psicologia. Neste artigo, reflicto, a partir da minha prática de patologista, sobre o sentido do diagnóstico morfológico e interrogo-me acerca de como um maior conhecimento das alterações morfológicas se relaciona com uma melhor compreensão das situaçōes patológicas. Sublinho a tensāo entre as dimensōes subjectiva e objectiva ao decidir, na incerteza, como é próprío do processo que leva ao diagnóstico. Defendo ainda a necessidade do raciocínio clínico para a razoabilidade de todo o diagnóstico. Starting from the novel "O alienista" by Machado de Assis, I aim at discussing on the "normal" and the "pathological", referring to Georges Canguilhem and his work The normal and the pathological. Trying to understand how medicine states the concept of "normal" and, as opposed to it, the concept of pathological, Canguilhems thought was influencing a wide range of knowledges, going from the understanding of the individuals and the valorisation of the normativity to the whole of questions concerning the trinomial ethics-politics-psychology. In this paper, I reflect, from my practice as pathologist, on the sense of the morphological diagnosis and I question myself how a dipper knowledge of morphological mutations relates to a better understanding of pathological situations. I highlight the tension between the subjective and objective dimension deciding with uncertainty, as it is peculiar of the process that leads to diagnosis. Also, I support the necessity of the clinical reasoning to the reasonability of every diagnosis. (shrink)

Metaphor abounds in both sign and spoken languages. However, in sign languages, languages in the visual-manual modality, metaphors work a bit differently than they do in spoken languages. In this paper we explore some of the ways in which metaphors in sign languages differ from metaphors in spoken languages. We address three differences: (a) Some metaphors are very common in spoken languages yet are infelicitous in sign languages; (b) Body-part terms are possible in very specific types of metaphors (...) in sign languages, but are not so restricted in spoken languages; (c) Similes in some sign languages are dispreferred in predicative positions in which metaphors are fine, in contrast to spoken languages where both can appear in these environments. We argue that these differences can be explained by two seemingly unrelated principles: the Double Mapping Constraint (Meir 2010), which accounts for the interaction between metaphor and iconicity in languages, and Croft's (2003) constraint regarding the autonomy and dependency of elements in metaphorical constructions. We further argue that the study of metaphor in the signed modality offers novel insights concerning the nature of metaphor in general, and the role of figurative speech in language. (shrink)

Even the simplest narratives combine multiple strands of information, integrating different characters and their actions by expressing multiple perspectives of events. We examined the emergence of referential shift devices, which indicate changes among these perspectives, in Nicaraguan Sign Language (NSL). Sign languages, like spoken languages, mark referential shift grammatically with a shift in deictic perspective. In addition, sign languages can mark the shift with a point or a movement of the body to a specified spatial location in the three-dimensional space (...) in front of the signer, capitalizing on the spatial affordances of the manual modality. We asked whether the use of space to mark referential shift emerges early in a new sign language by comparing the first two age cohorts of deaf signers of NSL. Eight first-cohort signers and ten second-cohort signers watched video vignettes and described them in NSL. Narratives were coded for lexical (use of words) and spatial (use of signing space) devices. Although the cohorts did not differ significantly in the number of perspectives represented, second-cohort signers used referential shift devices to explicitly mark a shift in perspective in more of their narratives. Furthermore, while there was no significant difference between cohorts in the use of non-spatial, lexical devices, there was a difference in spatial devices, with second-cohort signers using them in significantly more of their narratives. This suggests that spatial devices have only recently increased as systematic markers of referential shift. Spatial referential shift devices may have emerged more slowly because they depend on the establishment of fundamental spatial conventions in the language. While the modality of sign languages can ultimately engender the syntactic use of three-dimensional space, we propose that a language must first develop systematic spatial distinctions before harnessing space for grammatical functions. (shrink)

The study investigates the manifestation of the “IDEA-IS-AN-ENTITY” metaphor across the linguistic and manual modalities by the use of the object gesture in daily conversation, to understand the relationship between metaphorical conceptualization and the context of use. Two types of the entity metaphor were distinguished: “cross-modal entity metaphor” and “gesture-only entity metaphor.” For the former, the metaphor was expressed by metaphorical speech and the object gesture simultaneously. Among all of the 67 cross-modal instances, a wide variety of idea was (...) represented as referring, characterizing, and quantifying referents in speech. Manually, the object gesture was configured in numerous ways. The way the object gesture was configured reveals the facet of the metaphorical conceptualization the speaker focuses on during speaking, and the details about the real-time thinking of a metaphorical object in discourse. For the gesture-only entity metaphor, it was manifested in the single modality of gesture. Among all of the 73 gesture-only instances, the object gesture depicted a stretch of talk as discrete object mainly by configuring a spatial boundary with curled fingers. Metaphor of this type attests that the thinking of phrasal-clausal ideas as entities is as common as that of lexical ideas as entities in conversation. Importantly, the object gesture bears out the emergence of a phrasal or clausal idea being conceptualized as object in natural discourse. Together, the findings demonstrate the inseparability of metaphorical conceptualization from cognition and the context of use. (shrink)

Arbitrary communication systems can emerge from iconic beginnings through processes of conventionalisation via interaction. Here, we explore whether this process of conventionalisation occurs with continuous, auditory signals. We conducted an artificial signalling experiment. Participants either created signals for themselves, or for a partner in a communication game. We found no evidence that the speech-like signals in our experiment became less iconic or simpler through interaction. We hypothesise that the reason for our results is that when it is difficult to be (...) iconic initially because of the constraints of the modality, then iconicity needs to emerge to enable grounding before conventionalisation can occur. Further, pressures for discrimination, caused by the expanding meaning space in our study, may cause more complexity to emerge, again as a result of the restrictive signalling modality. Our findings have possible implications for the processes of conventionalisation possible in signed and spoken languages, as the spoken modality is more restrictive than the manual modality. (shrink)

Striking similarities across ape gestural repertoires suggest shared phylogenetic origins that likely provided a foundation for the emergence of language. We pilot a novel approach for exploring possible semantic universals across human and nonhuman ape species. In a forced‐choice task, n = 300 participants watched 10 chimpanzee gesture forms performed by a human and chose from responses that paralleled inferred meanings for chimpanzee gestures. Participants agreed on a single meaning for nine gesture forms; in six of these the agreed form‐meaning (...) pair response(s) matched those established for chimpanzees. Such shared understanding suggests apes' (including humans') gesturing shares deep evolutionary origins. (shrink)

1. Formal semantics in linguistics -- 2. Generalized quantifier theory -- 3. The interface between syntax and semantics -- 4. Anaphora, discourse, and modality -- 5. Focus, presupposition, and negation -- 6. Tense -- 7. Questions -- 8. Plurals -- 9. Computational semantics -- 10. Lexical semantics -- 11. Semantics and related domains.

Current conceptions of human language include a gestural component in the communicative event. However, determining how the linguistic and gestural signals are distinguished, how each is structured, and how they interact still poses a challenge for the construction of a comprehensive model of language. This study attempts to advance our understanding of these issues with evidence from sign language. The study adopts McNeill's criteria for distinguishing gestures from the linguistically organized signal, and provides a brief description of the linguistic organization (...) of sign languages. Focusing on the subcategory of iconic gestures, the paper shows that signers create iconic gestures with the mouth, an articulator that acts symbiotically with the hands to complement the linguistic description of objects and events. A new distinction between the mimetic replica and the iconic symbol accounts for the nature and distribution of iconic mouth gestures and distinguishes them from mimetic uses of the mouth. Symbiotic symbolization by hand and mouth is a salient feature of human language, regardless of whether the primary linguistic modality is oral or manual. Speakers gesture with their hands, and signers gesture with their mouths. (shrink)

Taboo terms offer a playground for linguistic creativity in language after language, and sign languages form no exception. The present paper offers the first investigation of taboo terms in sign languages from a cognitive linguistic perspective. We analyze the linguistic mechanisms that introduce offense, focusing on the combined effects of cognitive metonymy and iconicity. Using the Think Aloud Protocol, we elicited offensive or crass signs and dysphemisms from nine signers. We find that German Sign Language uses a variety of linguistic (...) means to introduce and enhance offense, many of which rely on iconic properties of the taboo sign. In conjunction with cross-linguistically common metonymic word-formation strategies, the degree of visual explicitness of a sign increases its potential to offend. Semantically similar taboo signs based on the same metonymic anchor but differing in their degree of iconicity also differ in offensiveness. This allows for creating dysphemisms and euphemisms via phonological changes to a sign. We further show that embodiment creates modality-enhanced ‘vicarious embarrassment’ in the viewer that results in the respective signs being judged obscene or offensive. Further, lexical blending and non-manual enhancement play a role in the creation of dysphemisms in DGS. Lastly, we propose that iconicity as a cognitive structuring principle of linguistic expressions constrains the possible semantic extensions of iconic taboo terms. (shrink)

This paper investigates the ways English speakers employ the predicates like, similar, and resemble to express similarity in natural speech. A corpus of 450 instances was created and manually coded, and an acceptability rating experiment was conducted. Converging evidence from the corpus analysis and the experiment shows that the three predicates occur with the same range of uses, but differ in their propensities to occur with particular dimensions of similarity. Specifically, like is associated with metaphorical comparisons, and resemble is associated (...) with visual comparisons. A synchronic account of these findings is developed, based on a distinction between conventionally encoded meaning and prototypical usage. A diachronic account is also proposed, highlighting the commonality in the predicates’ conceptual origins and the differences in their historical usage. This work has theoretical and methodological implications for the study of similarity. In particular, it raises the possibility that previous findings may be distorted due to a reliance on certain similarity predicates in the phrasing of experimental instructions and stimuli. It also ties into debates on synonymy, suggesting a shift in attention from a distinction between denotational and associative meaning, to the aforementioned distinction between conventional and prototypical meaning. (shrink)

Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. It considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, (...) independent study as a course text, it covers more material than is typically covered in an introductory course. -/- Topics include: translation, proofs, and trees for sentential and predicate logic with identity, definite descriptions, and functional terms; normal forms; proofs and trees for the principal normal modal systems; an introduction to second order and quantified modal logic; formal syntax and semantics; mathematical induction; metatheory for many of these systems; semantics and trees for free logic, intuitionistic logic, and three-valued and paraconsistent logics. -/- A companion website contains a detailed student solutions manual with a running commentary on all starred exercises and a set of editable slides for instructors to customize their courses. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)