The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of BI’s semantics. We (...) use this set-up as a basis for exploring how coalgebraic semantics can, in contrast to the basic denotational semantics, be used to describe the concrete operational choices that are an essential part of proof-search. The overall aim, toward which this paper can be seen as an initial step, is to develop a uniform, generic, mathematical framework for understanding the relationship between the deductive structure of logics and the control structures of the corresponding reductive paradigm. (shrink)

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is (...) also decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

The “problem of intentionality” from the vantage point of a representational understanding of mind is explaining what thoughts and beliefs are and how they guide behaviour. From an anti-representationalist perspective, on the other hand, on which cognition itself is taken to be a kind of action, intentionality is a capacity to engage in behaviour that is meaningfully directed toward or about some situation. That these are not in fact competing insights is obscured by the representational/anti-representational framing of the debate. This (...) paper begins the work of shifting the conversation in two ways: (1) by arguing that it is the commitment to internal representations, not the acknowledgement of a role for representation per se, that is problematic; and, (2) by describing an alternative, externalist, representational approach that draws on extended, embodied, enactive insights. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an (...) extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an (...) extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

The intention here is that of giving a formal underpinning to the idea of 'meaning-is-use' which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett-Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i. e. the so-called reduction rules. For that we suggest (...) an extension to the Curry-Howard interpretation which draws on the idea of labelled deduction, and brings back Frege's device of variable-abstraction to operate on the labels (i. e., proof-terms) alongside formulas of predicate logic. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.

In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a first-order formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the mean- ing of counting and choice by reducing these constructs to first-order formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated. We (...) compare the new language with the concept of a disjunc- tive program with aggregates introduced by Faber, Leone and Pfeifer, and discuss the possibility of implementing a frag- ment of the language by translating it into the input language of the answer set solver DLV. The language is also compared with cardinality constraint programs defined by Syrjänen. (shrink)

This article explores some fundamental issues of definition-based lexical semantic research through a critique of the Natural Semantic Metalanguage (NSM) theory of semantic and grammatical description (Wierzbicka 1996, Semantics. Primes and Universals, Oxford University Press, Oxford). NSM is criticized for attaching excessive importance to explanatory definition, for its adoption of the reductive requirement that a definiens be simpler than a definiendum, and for its use of ‘canonical contexts’ to disambiguate meaning. The principle of substitutability, according to which (...) a definition of a term is accepted if it can be substituted for the term itself, is also critically examined, and the theory’s use of syntactic phenomena as evidence for polysemy is shown to be inconsistent. Finally, suggestions that NSM may be a valid analytical method for only a subpart of the lexicon are rejected. (shrink)

Impaired performance in verbal fluency tasks is a frequent observation in Parkinson’s disease. As to the nature of the underlying cognitive deficit, it is commonly attributed to a frontal-type dysexecutive syndrome due to nigrostriatal dopamine depletion. Whereas dopaminergic medication typically improves VF performance in PD, e.g., by ameliorating impaired lexical switching, its effect on semantic network activation is unclear. Data from priming studies suggest that dopamine causes a faster decay of semantic activation spread. The aim of the current (...) study was to examine the impact of dopaminergic medication on the dynamic change of word frequency during VF performance as a measure of semantic spreading activation. To this end, we performed a median split analysis of word frequency during phonemic and semantic VF task performance in a PD group tested while receiving dopaminergic medication as well as after drug withdrawal, and in a sample of age-matched healthy volunteers. Dopaminergic medication in the PD group significantly affected phonemic VF with improved word production as well as increased error-rates. The expected decrease of word frequency during VF task performance was significantly smaller in the PD group ON medication than in healthy volunteers across semantic and phonemic VF. No significant group-difference emerged between controls and the PD group in the OFF condition. The comparison between both treatment conditions within the PD group did not reach statistical significance. The observed pattern of results indicates a faster decay of semantic network activation during lexical access in PD patients on dopaminergic medication. In view of improved word generation, this finding is consistent with a concept of more focused neural activity by an increased signal-to-noise ratio due to dopaminergic neuromodulation. However, the effect of dopaminergic stimulation on VF output suggests a trade-off between these beneficial effects and increased error-rates. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical (...) debate on the nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

Causal theories of content, a popular family of approaches to defining the content of mental states, commonly run afoul of two related and serious problems that prevent them from providing an adequate theory of mental content—the misrepresentation problem and the disjunction problem. In this paper, I present a causal theory of content, built on information theoretic tools, that solves these problems and provides a viable model of mental content. This is the greatest surprise reduction theory of content, which identifies (...) the content of a signal as the event the surprisal of which is most reduced by that signal. Conceptually, this amounts to the claim that the content of a signal is the event the probability of which has increased by the largest proportion, or the event that the signal makes the most less surprising to us. I develop the greatest surprise reduction theory of content in four stages. First, I introduce the general project of causal theories of content, and the challenges presented to this project by the misrepresentation and disjunction problems. Next, I review two recent and prominent causal theories of content and demonstrate the serious challenges faced by these approaches, both clarifying the need for a solution to the misrepresentation and disjunction problems and providing a conceptual background for the greatest surprise reduction theory. Then, I develop the greatest surprise reduction theory of content, demonstrate its ability to resolve the misrepresentation and disjunction problems, and explore some additional applications it may have. Finally, I conclude with a discussion of a particularly difficult challenge that remains to be addressed—the partition problem—and sketch a path to a potential solution. (shrink)

It is assumed that a Kripke–Joyal semantics \({\mathcal{A} = \left\langle \mathbb{C},{\rm Cov}, {\it F},\Vdash \right\rangle}\) has been defined for a first-order language \({\mathcal{L}}\) . To transform \({\mathbb{C}}\) into a Heyting algebra \({\overline{\mathbb{C}}}\) on which the forcing relation is preserved, a standard construction is used to obtain a complete Heyting algebra made up of cribles of \({\mathbb{C}}\) . A pretopology \({\overline{{\rm Cov}}}\) is defined on \({\overline{\mathbb{C}}}\) using the pretopology on \({\mathbb{C}}\) . A sheaf \({\overline{{\it F}}}\) is made up of sections of (...) F that obey functoriality. A forcing relation \({\overline{\Vdash}}\) is defined and it is shown that \({\overline{\mathcal{A}} = \left\langle \overline{\mathbb{C}},\overline{\rm{Cov}},\overline{{\it F}}, \overline{\Vdash} \right\rangle }\) is a Kripke–Joyal semantics that faithfully preserves the notion of forcing of \({\mathcal{A}}\) . That is to say, an object a of \({\mathbb{C}Ob}\) forces a sentence with respect to \({\mathcal{A}}\) if and only if the maximal a-crible forces it with respect to \({\overline{\mathcal{A}}}\) . This reduces a Kripke–Joyal semantics defined over an arbitrary site to a Kripke–Joyal semantics defined over a site which is based on a complete Heyting algebra. (shrink)

Dynamic and proof-conditional approaches to discourse (exemplified by Discourse Representation Theory and Type-Theoretical Grammar, respectively) are related through translations and transitions labeled by first-order formulas with anaphoric twists. Type-theoretic contexts are defined relative to a signature and instantiated modeltheoretically, subject to change.

Poverty reduction strategy papers (PRSPs) present a recipient country’s program of intent for the utilization of World Bank loans and grants to alleviate debt under the bank’s programs of action for poverty reduction in highly indebted poor countries (HIPCs). This article argues that structural transformation is a prerequisite for poverty reduction in Zambia. However, the Zambian PRSP is largely informed by mainstream thinking on poverty and livelihoods. It champions a neoliberal program constructed on the sanctity of the (...) market and seeks to maintain the very structural processes that engender poverty. Because it fails to break, conceptually and methodologically, from past program failures, the PRSP is likely to be just the latest installment in the ever-changing fashionable semantics of the “development community.” The article examines the conceptual and methodological failures of the Zambian PRSP particularly with respect to the measurement of poverty and the concept of participation. (shrink)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...) establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

This paper introduces three model-theoretic constructions for generalized Epstein semantics: reducts, ultramodels and $\textsf {S}$ -sets. We apply these notions to obtain metatheoretical results. We prove connective inexpressibility by means of a reduct, compactness by an ultramodel and definability theorem which states that a set of generalized Epstein models is definable iff it is closed under ultramodels and $\textsf {S}$ -sets. Furthermore, a corollary concerning definability of a set of models by a single formula is given on the basis of (...) the main theorem and the compactness theorem. We also provide an example of a natural set of generalized Epstein models which is undefinable. Its undefinability is proven by means of an $\textsf {S}$ -set. (shrink)

The article presents a full proof‐theoretic semantics for natural deduction based on an extended inversion principle: the elimination rule for an operator q may invert the introduction rule for q, but also vice versa, the introduction rule for a connective q may invert the elimination rule for q. Such an inversion—extending Prawitz' concept of inversion—gives the following theorem: Inversion for two rules of operator q (intro rule, elim rule) exists iff a reduction of a maximum formula for q exists. (...) The inversion theorem is specified to two logics, Lambek calculus (LC) and intuitionistic linear logic (ILL), with four propositional connectives: two multiplicatives (implication and conjunction) and two additives (conjunction and disjunction), with two quantifiers and two modals. LC is defined by using elimination rules by composition. ILL is defined by using usual general elimination rules. Elimination rules by composition are an exciting alternative to general elimination rules; in some cases, they do not need permutations. (shrink)

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions (...) of a reducing theory T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

Semantic dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g., infer a certain way. Its main problem is that it seems to have so many and disparate exceptions. People can fail to infer as required due to lack of logical acumen, intoxication, confusion, deviant theories, neural malfunctioning, and so on. I present a theory stating possession conditions of concepts that are counterfactuals, rather (...) than disposition attributions, but which is otherwise similar to inferentialist versions of dispositionalism. I argue that it can handle all the exceptions discussed in the literature without recourse to ceteris paribus clauses. Psychological exceptions are handled by suitably undemanding requirements (unlike that of giving the sum of any two numbers) and by setting the following two preconditions upon someone’s making the inference: that she considers the inference and has no motivating reason against it. The non-psychological exceptions, i.e., cases of neural malfunctioning, are handled by requiring that the counterfactuals be true sufficiently often during the relevant interval. I argue that this accommodates some important intuitions about concept possession, in particular, the intuition that concept possession is vague along a certain dimension. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical (...) debate on the nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

This paper argues that the Husserl—Heidegger relationship is systematically misunderstood when framed in terms of a distinction between internalism and externalism. Both philosophers, it is argued, employ the phenomenological reduction to immanence as a fundamental methodological instrument. After first outlining the assumptions regarding inner and outer and the individual and the social from which recent epistemological interpretations of phenomenology begin, I turn to the question of Husserl's internalism. I argue that Husserl can only be understood as an internalist on (...) the assumption that immanence equates with internal. This, however, is not the case as can be seen once the reduction is understood not as setting aside the existence of the world, but rather a reflection on its meaning. Turning to Heidegger, I argue that his commitment to a form of the phenomenological reduction precludes him from being either a semantic or a social externalist. The place of authenticity and the first person perspective in his work derive from his phenomenological commitments, which can be seen in his accounts of discourse and language and of falling (Verfallen). I then go on to briefly outline a more plausible basis for understanding the difference between Husserl's and Heidegger's phenomenologies in terms of their respective emphases on logic and on poetics. (shrink)

Many philosophers insist that moral facts or properties play no role in explaining (non-normative) natural phenomena. The problem of moral explanation has raised metaphysical, semantic and epistemic challenges to contemporary moral realism. In my dissertation, I attempt to vindicate the explanatory efficacy of moral properties, while at the same time respecting the autonomy and normativity of morality. In doing so, I will advocate a sort of non-reductive ethical naturalism, according to which moral properties are natural properties (in the sense (...) that they are open to empirical investigation), and yet remain irreducible to non-normative natural properties, such as psychological, biological, and sociological properties. More specifically, I develop a form of moral functionalism to vindicate moral explanation. Moral functionalism understands moral properties as second-order, functional properties, the natures of which are characterized in terms of functional roles. My version of moral functionalism has two particular features. First, it is a form of a posteriori moral functionalism. The moral theory used to characterize the functional roles of moral properties can only be discovered by appeal to empirical investigation (for this reason, my a posteriori version of moral functionalism is a sort of ethical naturalism). Second, it is a holistic version of moral functionalism. The functional role of a moral property cannot be identified solely in terms of non-normative properties; rather, it essentially involves a network of connections to both non-normative and normative properties (for this reason, my holistic version of moral functionalism is a sort of ethical anti-reductionism). It is important to note that the question of whether moral properties have explanatory power bears on the question of what explanation or explanatoriness is. In my dissertation, I attempt to show that my vindication of moral explanation presupposes a plausible account of explanation. Obviously I cannot discuss all theories of explanation; my dissertation will rather focus on two influential accounts of explanation: the causalist model and the unificationist model. Then I argue that moral properties understood as functional properties of the kind I have described can do causal-explanatory work and play a distinctive unifying role. (shrink)

It is argued that although George Bealer's influential ‘Self-Consciousness argument’ refutes standard versions of reductive functionalism (RF), it fails to generalize in the way Bealer supposes. To wit, he presupposes that any version of RF must take the content of ‘pain’ to be the property of being in pain (and so on), which is expressly rejected in independently motivated versions of conceptual role semantics (CRS). Accordingly, there are independently motivated versions of RF, incorporating CRS, which avoid Bealer's main type of (...) refutation. I focus particularly on one such theory, which takes concepts to be event types that are individuated by their psychological roles, which has the resources of responding to each of the more specific worries Bealer expresses. (shrink)

Increasing computational power and improving deep learning methods have made computer vision technologies pervasively common in urban environments. Their applications in policing, traffic management, and documenting public spaces are increasingly common (Ridgeway 2018, Coifman et al. 1998, Sun et al. 2020). Despite the often-discussed biases in the algorithms' training and unequally borne benefits (Khosla et al. 2012), almost all applications similarly reduce urban experiences to simplistic, reductive, and mechanistic measures. There is a lack of context, depth, and specificity in these (...) practices that enables semantic knowledge or analysis within urban contexts, especially within the context of using and occupying urban space. This paper will critique existing uses of artificial intelligence and computer vision in urban practices to propose a new framework for understanding people, action, and public space. This paper revisits Geertz's (1973) use of thick descriptions in generating interpretive theories of culture and activity and uses this lens to establish a framework to approach evaluating the varied uses of computer vision technologies that weigh meaning. By discussing cases of implemented examples of urban computer vision—from LinkNYC and Numina's urban measurements to the Detroit Police's use of DataWorks Plus's facial recognition technology—it proposes a framework for evaluating the thickness of the algorithm's conclusions against the computational method's complexity required to produce that outcome. Further, we discuss how the framework's positioning may differ (and conflict) between different users of the technology, from engineer to urban planner and policymaker, to citizen. This paper also discusses how the current use and training of deep learning algorithms and how this process limits semantic learning and proposes three potential methodologies toward gaining a more contextually specific, urban-semantic, description of urban space relevant to urbanists. This paper contributes to the critical conversations regarding the proliferation of artificial intelligence by challenging the current applications of these technologies in the urban environment by highlighting their failures within this context while also proposing an evolution of these algorithms that may ultimately make them sensitive and useful within this spatial and cultural milieu. (shrink)

Research from psychology, neurobiology and behavioral economics indicates that a binary view of motivation, based on approach and avoidance, may be too reductive. Instead, a literature review suggests that at least seven distinct motives are likely to affect human decisions: “consumption/resource seeking,” “care,” “affiliation,” “achievement,” “status-power,” “threat approach” (or anger), and “threat avoidance” (or fear). To explore the conceptual distinctness and relatedness of these motives, we conducted a semantic categorization task. Here, participants were to assign provided words to one (...) of the motives. By applying principal component analysis to the categorization assignments we represent the semantic inter-relations of these motives on a two-dimensional space, a “semantic atlas.” This atlas suggests that, while care and affiliation are conceptually close, affiliation is closer to threat avoidance (or fear); opposite to these motives we find achievement, consumption and power, with the latter lying closer to threat approach (or anger). In a second study, we asked participants to rate how well the motive-specific words obtained in the first study described their currently experienced feelings. We find that semantically close motives are also more likely to be experienced together, that is, we replicate most of the semantic relations in the “subjective atlas.” We discuss our findings in comparison to other multi-dimensional models of motivation, which show clear similarities. In addition to these motivational atlases, we provide a database of motive-specific words, together with the valence and arousal scores. These can be used for future research on the influence of motives on decision making. (shrink)

This chapter starts with Goodman's project, saying what his aim was, spelling out the resources that he allowed himself to use in order to accomplish this aim, and explaining why the aim could not be accomplished with these resources. The author considers Goodman's response to the acknowledged failure of his initial attempt at analysis: how he proposed to redefine his Humean project. The chapter sketches David Lewis's project, which has two parts: an abstract formal semantic analysis of conditionals, and (...) an attempt to explain the primitive parameters of the semantic models in a way that is austere enough to satisfy the Humean structures. The author argues that Lewis does not succeed in identifying a suitable base for a reduction of counterfactuals and other causal notions. The chapter concludes with a brief remark on the problems that remain if we reject the project of Humean reduction. (shrink)

Multiply realizable properties are those whose realizers are physically diverse. It is often argued that theories which contain them are ipso facto irreducible. These arguments assume that physical explanations are restricted to the most specific descriptions possible of physical entities. This assumption is descriptively false, and philosophically unmotivated. I argue that it is a holdover from the late positivist axiomatic view of theories. A semantic view of theories, by contrast, correctly allows scientific explanations to be couched in the most (...) perspicuous, powerful language available. On a semantic view, traditional notions of multiple realizability are thus very hard to motivate. At best, one must abandon either the idea that multiple realizability is an interesting scientific notion, or else admit that multiply realizable properties do not automatically block scientific reductions. (shrink)

David Papineau's model of scientific reduction, contrary to his intent, appears to enable a naturalist realist account of the primitive normativity involved in a biological adaptation's being “for” this or that (say the eye's being for seeing). By disabling the crucial anti‐naturalist arguments against any such reduction, his model would support a cogni‐tivist semantics for normative claims like “The heart is for pumping blood, and defective if it doesn't.” No moral claim would follow, certainly. Nonetheless, by thus “pressing (...) from below” we may learn something about moral normativity. For instance, suppose non‐cognitivists like Mackie are right that the semantics of normative claims should be “unified”: if the semantics of moral claims is non‐cognitivist, so too is that of all normative claims. Then, assuming that a naturalist reduction does yield a sound cognitivist account of the primitive normativity, it would follow that our semantics of moral claims is cognitivist as well. (shrink)

The paper looks at the semantics and ontology of dispositions in the light of recent work on the subject. Objections to the simple conditionals apparently entailed by disposition statements are met by replacing them with so-called 'reduction sentences' and some implications of this are explored. The usual distinction between categorical and dispositional properties is criticised and the relation between dispositions and their bases examined. Applying this discussion to two typical cases leads to the conclusion that fragility is not a (...) real property and that, while both temperature and its bases are, this does not generate any problem of overdetermination. (shrink)

The semantic fluency task is a widely used clinical tool in the diagnostic process of Alzheimer's disease. The task requires efficient mapping of the semantic space to produce as many items as possible within a semantic category. We examined whether healthy volunteers and patients with early Alzheimer's disease take advantage of and travel in the semantic space differently. With focus on the animal fluency task, we sought to emulate the detailed structure of the multidimensional semantic (...) space by utilizing word2vec-method from the natural language processing domain. To render the resulting multidimensional semantic space visually comprehensible, we applied a dimensionality reduction algorithm, which enabled a straightforward division of the semantic space into sub-categories. Moving in semantic space was quantified with the number of items created, sub-categories visited, and switches and returns to these sub-categories. Multinomial logistic regression models were used to predict the diagnostic group with these independent variables. We found that returning to a sub-category provided additional information, besides the number of words produced in the task, to differentiate patients with Alzheimer's dementia from both amnestic Mild Cognitive Impairment patients and healthy controls. The results suggest that the frequency of returning to a sub-category may serve as an additional aid for clinicians in diagnosing early Alzheimer's disease. Moreover, our results imply that the combination of word2vec and subsequent t-SNE-visualization may offer a valuable tool for examining the semantic space and its sub-categories. (shrink)

We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason with eigenworlds (i.e., generic representatives of worlds) in an arbitrary model. This reasoning is captured by a sequent calculus for a _meta_-logic (in this case, first-order classical logic) expressive enough to capture the semantics of the object-logic. Essentially, one has a calculus of validity for the (...) object-logic. The method proceeds through the perspective of reductive logic (as opposed to the more traditional paradigm of deductive logic), using the space of reductions as a medium for showing the behavioural equivalence of reduction in the sequent calculus for the object-logic and in the validity calculus. Rather than study the technique in general, we illustrate it for the logic of Bunched Implications (BI), thus IPL and MILL (without negation) are also treated. Intuitively, BI is the free combination of intuitionistic propositional logic and multiplicative intuitionistic linear logic, which renders its meta-theory is quite complex. The literature on BI contains many similar, but ultimately different, algebraic structures and satisfaction relations that either capture only fragments of the logic (albeit large ones) or have complex clauses for certain connectives (e.g., Beth’s clause for disjunction instead of Kripke’s). It is this complexity that motivates us to use BI as a case-study for this approach to semantics. (shrink)

In the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations in the newly (...) introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.prepared by Sandro Márcio da Silva Preto.E-mail: [email protected]:https://doi.org/10.11606/T.45.2021.tde-17062021-163257. (shrink)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of (...) metalogical sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (shrink)

If semantic consequence is analyzed with extensive games, logical reasoning can be accounted for by looking at how players solve entailment games. However, earlier approaches to game semantics cannot achieve this reduction, by want of explicitly dened preferences for players. Moreover, although entailment games can naturally translate the idea of argumentation about a common ground, a cognitive interpretation is undermined by the complexity of strategic reasoning. We thus describe a class of semantic extensive entailment game with algorithmic (...) players, who have preferences for parsimonious spending of computational resources and thus compute partial strategies under qualitative uncertainty about future histories. We prove the existence of local preferences for moves and of strategic fixpoints that allow to map game-trees to tableaux proofs, and exhibit a strategy prole that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We then discuss the correspondence between proof heuristics and strategies in our games, the relations of our games to gts, and possible extensions to other entailment relations. We conclude that the main interest of our result lies in the possibility to bridge argumentative and cognitive models of logical reasoning, rather than in new meta-theoretic results. All proofs are given in appendix. (shrink)

Dynamic epistemic logic (DEL) is a multi-modal logic for reasoning about the change of knowledge in multi-agent systems. It extends epistemic logic by a modal operator for actions which announce logical formulas to other agents. In Hilbert-style proof calculi for DEL, modal action formulas are reduced to epistemic logic, whereas current sequent calculi for DEL are labelled systems which internalize the semantic accessibility relation of the modal operators, as well as the accessibility relation underlying the semantics of the actions. (...) We present a novel cut-free ordinary sequent calculus, called |$ \textbf{G4}_{P,A}[] $|⁠, for propositional DEL. In contrast to the known sequent calculi, our calculus does not internalize the accessibility relations, but—similar to Hilbert style proof calculi—action formulas are reduced to epistemic formulas. Since no ordinary sequent calculus for full S5 modal logic is known, the proof rules for the knowledge operator and the Boolean operators are those of an underlying S4 modal calculus. We show the soundness and completeness of |$ \textbf{G4}_{P,A}[] $| and prove also the admissibility of the cut-rule and of several other rules for introducing the action modality. (shrink)

David Papineau’s model of scientific reduction, contrary to his intent, appears to enable a naturalist realist account of the primitive normativity involved in a biological adaptation’s being “for” this or that (say the eye’s being for seeing). By disabling the crucial anti-naturalist arguments against any such reduction, his model would support a cognitivist semantics for normative claims like “The heart is for pumping blood, and defective if it doesn’t.” No moral claim would follow, certainly. Nonetheless, by thus “pressing (...) from below” we may learn something about moral normativity. For instance, suppose non-cognitivists like Mackie are right that the semantics of normative claims should be “unified”: if the semantics of moral claims is non-cognitivist, so too is that of all normative claims. Then, assuming that a naturalist reduction does yield a sound cognitivist account of the primitive normativity, it would follow that our semantics of moral claims is cognitivist as well. (shrink)

Applying machine learning algorithms to automatically infer relationships between concepts from large-scale collections of documents presents a unique opportunity to investigate at scale how human semantic knowledge is organized, how people use it to make fundamental judgments (“How similar are cats and bears?”), and how these judgments depend on the features that describe concepts (e.g., size, furriness). However, efforts to date have exhibited a substantial discrepancy between algorithm predictions and human empirical judgments. Here, we introduce a novel approach to (...) generating embeddings for this purpose motivated by the idea that semantic context plays a critical role in human judgment. We leverage this idea by constraining the topic or domain from which documents used for generating embeddings are drawn (e.g., referring to the natural world vs. transportation apparatus). Specifically, we trained state-of-the-art machine learning algorithms using contextually-constrained text corpora (domain-specific subsets of Wikipedia articles, 50+ million words each) and showed that this procedure greatly improved predictions of empirical similarity judgments and feature ratings of contextually relevant concepts. Furthermore, we describe a novel, computationally tractable method for improving predictions of contextually-unconstrained embedding models based on dimensionality reduction of their internal representation to a small number of contextually relevant semantic features. By improving the correspondence between predictions derived automatically by machine learning methods using vast amounts of data and more limited, but direct empirical measurements of human judgments, our approach may help leverage the availability of online corpora to better understand the structure of human semantic representations and how people make judgments based on those. (shrink)

This paper confronts a certain modern view of the relation between semantics and ontology with that of the late-medieval nominalist philosophers, William Ockham and John Buridan. The modern view in question is characterized in terms of what is called here “the thesis of onto-semantic parallelism,” which states that the primitive (indefinable) categorematic concepts of our semantics mark out the primary entities in reality. The paper argues that, despite some apparently plausible misinterpretations to the contrary, the late-medieval nominalist program of (...) “ontological reduction” was not driven by considerations that try to “read off” ontology from semantic analysis or those that try to identify semantic primitives in their search for ontological primitives. The medieval authors presented a much more flexible, dynamic view of “Aristotelian naturalism,” which challenges both of the unappealing modern alternatives of “conceptual tribalism” and “conceptual imperialism.”. (shrink)

What makes our utterances mean what they do? In this work I formulate and justify a structural constraint on possible answers to this key question in the philosophy of language, and I show that accepting this constraint leads naturally to the adoption of an algebraic formalization of truth-theoretic semantics. I develop such a formalization, and show that applying algebraic methodology to the theory of meaning yields important insights into the nature of language. ;The constraint I propose is, roughly, this: the (...) meaning of an utterance of a natural language sentence is derived from the place of that sentence within a system that includes other sentences, and is structured in virtue of primitive semantic facts about complete sentences. This constraint calls for a formal semantics program where the meaning of natural language sentences is represented by an appropriate assignment of the elements of an algebraic structure to sentences, an assignment that represents facts concerning complete sentences. I call the above constraint 'The Algebraic Thesis', and the corresponding formal semantics program 'Algebraic Semantics.' ;I introduce AT by carving it out of the holistic views of language of Quine and Davidson, and I show that it is independent of other important features of these philosophers' views. I then argue for AT, taking into account recent work by Brandom, Dummett, Fodor and Lepore, Gaifman and Perry. In developing Algebraic Semantics I present structures of two basic types: Boolean algebras and cylindric algebras; these structures are construed in the context of AT in a novel way: they are treated as applying to classes of sentences as numbers apply to physical objects in measurement. Applying algebraic methodology to formal semantics and to the theory of meaning, I develop these results: ; An account of the semantics of necessity and possibility that avoids both Quine's dismissal of these notions and their reduction by David Lewis to quantification over possible worlds; ; The application of the model-theoretic notion of expansion to capture the process of our learning progressively more of the meaning of expressions in our first languages. (shrink)

The notion of reduction in the natural sciences has been assimilated to the notion of inter-theoretical explanation. Many philosophers of science (following Nagel) have held that the apparently ontological issues involved in reduction should be replaced by analyses of the syntactic and semantic connections involved in explaining one theory on the basis of another. The replacement does not seem to have been especially successful, for we still lack a plausible account of inter-theoretical explanation. I attempt to provide (...) one. (shrink)