This paper proposes a formalization of ability that is motivated in part by linguistic considerations and by the philosophical literature in action theory and the logic of ability, but that is also meant to match well with planning formalisms, and so to provide an account of the role of ability in practical reasoning. Some of the philosophical literature concerning ability, and in particular [Austin, 1956], suggests that some ways of talking about ability are context-dependent. I propose a way of (...) formalizing this dependency. (shrink)

Drawing upon research in philosophical logic, linguistics and cognitive science, this study explores how our ability to use and understand language depends upon our capacity to keep track of complex features of the contexts in which we converse.

This is part of a larger project that is motivated in part by linguistic considerations and by the philosophical literature in action theory and the logic of ability, but that is also meant to suggest ways in which planning formalisms could be modified to provide an account of the role of ability in planning and practical reasoning.

In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee \ given \” with a semantics based not on standard epistemic models but on labeled transition systems that represent the agent’s knowledge of his own abilities. The semantics is inspired by conformant planning in AI. A sound and (...) complete proof system is given to capture valid reasoning patterns, which highlights the compositional nature of “knowing how”. The logical language is further extended to handle knowing how to achieve a goal while maintaining other conditions. (shrink)

How much linguistic understanding is required for testimonial knowledge acquisition? One answer is that, so long as we grasp the content expressed by the speaker, it does not matter if our understanding of it is poor. Call this the ‘Liberal View’ of testimony. This approach looks especially promising when combined with the thesis that we share a public language that makes it easy to grasp the right content. In this paper, I argue that this picture is epistemically problematic. Poor (...) linguistic understanding undermines our ability to recognise evidence and counterevidence for the testimonial content. Because of this, in many cases in which a hearer’s understanding is poor, her resultant testimonial belief will lack sufficient warrant to qualify as knowledge. Given that we often do not possess a sufficiently good understanding of the testimony we consume, I argue that we acquire far less knowledge through testimony than the Liberal View suggests. (shrink)

The received wisdom on ability modals is that they differ from their epistemic and deontic cousins in what inferences they license and better receive a universal or conditional analysis instead of an existential one. The goal of this paper is to sharpen the empirical picture about the semantics of ability modals, and to propose an analysis that explains what makes the can of ability so special but that also preserves the crucial idea that all uses of can share a common (...) lexical semantics. The resulting framework combines tools and techniques from dynamic and inquisitive semantics with insights from the literature of the role of agency in deontic logic. It explains not only why the can of ability, while essentially being an existential modal operator, sometimes resists distribution over disjunction and interacts with its duals in particular and hitherto unnoticed ways, but also has a tendency to license free choice inferences. (shrink)

Most agents can acquire information about their environments as they operate. A good plan for such an agent is one that not only achieves the goal, but is also executable, i.e., ensures that the agent has enough information at every step to know what to do next. In this paper, we present a formal account of what it means for an agent to know how to execute a plan and to be able to achieve a goal. Such a theory is (...) a prerequisite for producing specifications of planners for agents that can acquire information at run time. It is also essential to account for cooperation among agents. Our account is more general than previous proposals, correctly handles programs containing loops, and incorporates a solution to the frame problem. It can also be used to prove programs containing sensing actions correct. (shrink)

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology (...) is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

“Logic” entails both a toolkit for dealing with situations requiring precision, and a prescription for a type of public reasoning. A sufficiently extended society facing a stream of genuinely novel opportunities and challenges will benefit from an ability to generate and encourage the use of such reasoning systems to deal with these opportunities and challenges. The study of “logic” is the result of using the toolkit on itself, which would appear to be a necessary and not unnatural step for a (...) society developing sufficient familiarity with the toolkit. Many societies have developed something like logic, and past and present use of logic-like toolkits in learning situations and transmission of skills suggests that many societies will develop something like logic. (shrink)

Mathematical game theory has been embraced by a variety of scholars: social scientists, biologists, linguists, and now, increasingly, logicians. This volume illustrates the recent advances of game theory in the field. Logicians benefit from things like game theory's ability to explain informational independence between connectives; meanwhile, game theorists have even begun to benefit from logical epistemic analyses of game states. In concert with such pioneering work, this volume also present surprising developments in classical fields, including first-order logic and set (...) theory. (shrink)

Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition93, 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar implicatures: Experiments at the semantics-pragmatics interface. Cognition, 86, 253-282; Hurewitz, F., Papafragou, A., Gleitman, L., Gelman, R. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development, 2, 76-97; Huang, Y. T., Snedeker, (...) J., Spelke, L. (submitted for publication). What exactly do numbers mean?]. Specifically, these studies have shown that data from experimental investigations of child language can be used to illuminate core theoretical issues in the semantic and pragmatic analysis of number terms. In this article, I extend this approach to the logico-syntactic properties of number words, focusing on the way numerals interact with each other (e.g. Three boys are holding two balloons) as well as with other quantified expressions (e.g. Three boys are holding each balloon). On the basis of their intuitions, linguists have claimed that such sentences give rise to at least four different interpretations, reflecting the complexity of the linguistic structure and syntactic operations involved. Using psycholinguistic experimentation with preschoolers (n=32) and adult speakers of English (n=32), I show that (a) for adults, the intuitions of linguists can be verified experimentally, (b) by the age of 5, children have knowledge of the core aspects of the logical syntax of number words, (c) in spite of this knowledge, children nevertheless differ from adults in systematic ways, (d) the differences observed between children and adults can be accounted for on the basis of an independently motivated, linguistically-based processing model [Geurts, B. (2003). Quantifying kids. Language Acquisition, 11(4), 197-218]. In doing so, this work ties together research on the acquisition of the number vocabulary with a growing body of work on the development of quantification and sentence processing abilities in young children [Geurts, 2003; Lidz, J., Musolino, J. (2002). Children's command of quantification. Cognition, 84, 113-154; Musolino, J., Lidz, J. (2003). The scope of isomorphism: Turning adults into children. Language Acquisition, 11(4), 277-291; Trueswell, J., Sekerina, I., Hilland, N., Logrip, M. (1999). The kindergarten-path effect: Studying on-line sentence processing in young children. Cognition, 73, 89-134; Noveck, I. (2001). When children are more logical than adults: Experimental investigations of scalar implicature. Cognition, 78, 165-188; Noveck, I., Guelminger, R., Georgieff, N., & Labruyere, N. (2007). What autism can tell us about every. . . not sentences. Journal of Semantics,24(1), 73-90. On a more general level, this work confirms the importance of integrating formal and developmental perspectives [Musolino, 2004], this time by highlighting the explanatory power of linguistically-based models of language acquisition and by showing that the complex structure postulated by linguists has important implications for developmental accounts of the number vocabulary. (shrink)

It is often assumed that the capability to make inferences requires language. Against this assumption, I claim that inferential abilities do not necessarily require a language. On the contrary, certain cartographic systems could be used to explain some forms of inferences, and they are capable of warranting rational relations between contents they represent. By arguing that certain maps, as well as sentences, are adequate for inferential processes, I do not mean to neglect that there are important differences between maps (...) and sentences. Instead, the purpose of this paper is to highlight interesting distinctions that might affect the way that cartographic thinking works. (shrink)

In broadest terms, this thesis is concerned to answer the question of whether the view that arithmetic is analytic can be maintained consistently. Lest there be much suspense, I will conclude that it can. Those who disagree claim that accounts which defend the analyticity of arithmetic are either unable to give a satisfactory account of the foundations of mathematics due to the incompleteness theorems, or, if steps are taken to mitigate incompleteness, then the view loses the ability to account for (...) the applicability of mathematics in the sciences. I will show that this criticism is not successful against every view whereby arithmetic is analytic by showing that the brand of "conventionalism" about mathematics that Rudolf Carnap advocated in the 1930s, especially in Logical Syntax of Language, does not suffer from these difficulties. There, Carnap develops an account of logic and mathematics that ensures the analyticity of both. It is based on his famous "Principle of Tolerance", and so the major focus of this thesis will to defend this principle from certain criticisms that have arisen in the 80 years since the book was published. I claim that these criticisms all share certain misunderstandings of the principle, and, because my diagnosis of the critiques is that they misunderstand Carnap, the defense I will give is of a primarily historical and exegetical nature. Again speaking broadly, the defense will be split into two parts: one primarily historical and the other argumentative. The historical section concerns the development of Carnap's views on logic and mathematics, from their beginnings in Frege's lectures up through the publication of Logical Syntax. Though this material is well-trod ground, it is necessary background for the second part. In part two we shift gears, and leave aside the historical development of Carnap's views to examine a certain family of critiques of it. We focus on the version due to Kurt Gödel, but also explore four others found in the literature. In the final chapter, I develop a reading of Carnap's Principle - the `wide' reading. It is one whereby there are no antecedent constraints on the construction of linguistic frameworks. I argue that this reading of the principle resolves the purported problems. Though this thesis is not a vindication of Carnap's view of logic and mathematics tout court, it does show that the view has more plausibility than is commonly thought. (shrink)

We demonstrate ways to incorporate nondeterminism in a system designed to formalize the reasoning of agents concerning their abilities and the results of the actions that they may perform. We distinguish between two kinds of nondeterministic choice operators: one that expresses an internal choice, in which the agent decides what action to take, and one that expresses an external choice, which cannot be influenced by the agent. The presence of abilities in our system is the reason why the (...) usual approaches towards nondeterminism cannot be used here. The semantics that we define for nondeterministic actions is based on the idea that composite actions are unravelled in the strings of atomic actions and tests that constitute them. The main notions used in defining this semantics are finite computation sequences and finite computation runs of actions. The results that we obtain meet our intuitions regarding events and abilities in the presence of nondeterminism. (shrink)

If a conclusion was reached that creatures without a language capability exhibit some form of a capability for logic, this would shed a new light on the relationship between logic, language, and thought. Recent experimental attempts to test whether some animals, as well as pre-linguistic human infants, are capable of exclusionary reasoning are taken to support exactly that conclusion. The paper discusses the analyses and conclusions of two such studies: Call’s (2004) two cups task, and Mody and Carey’s (2016) (...) four cups task. My paper exposes hidden assumptions within these analyses, which enable the authors to settle on the explanation which assigns logical capabilities to the participants of the studies, as opposed to the explanations which do not. The paper then demonstrates that the competing explanations of the experimental results are theoretically underdeveloped, rendering them unclear in their predictions concerning the behavior of cognitive subjects, and thus difficult to distinguish by use of experiments. Additionally, it is questioned whether the explanations are rivals at all, i.e. whether they compete to explain the cognitive processes of the same level. The contribution of the paper is conceptual. Its aim is to clear up the concepts involved in these analyses, in order to avoid oversimplified or premature conclusions about the cognitive abilities of pre- and non-linguistic creatures. It is also meant to show that the theoretical space surrounding the issues involved might be much more diverse and unknown than many of these studies imply. (shrink)

The competence of humans to create and apply constructs of reality far exceeds that of any other animal species. Their ability to consciously manipulate such models seems unique, but it remains unknown how these abilities were initially acquired and then developed. Most individuals hold strong, culturally-anchored beliefs that their particular reality is true, a viewpoint challenged by the observation that all such constructs are different. They reflect not reality, but each individual’s life experiences. Collectively they facilitated the development of (...) hominins to unprecedented cultural and cognitive complexity. However, it remains entirely unknown how the human brain manages to create a model of the external world from the signals provided by sensory equipment and proprioceptors. This paper examines the roles of exograms in this development, as they are considered to be the only tangible connection between the brain, the faculties of sentience and the external world. Competency in exogram use became a crucial natural selection factor for humans and even overcame the human brain atrophy of the final Pleistocene and the Holocene. Under favourable conditions, some forms of exograms are capable of surviving from the deep time of human evolution. The paper follows their trail back in time to gain some insights into the developments that gave rise to human awareness, self-consciousness and Theory of Mind as we understand them. Specific archaeological finds and notions about sentient capabilities of hominins are presented in a search for exogram use in the course of human evolution. It results in a model that explains with clarity not only the course of the human journey but also the underlying reasons for the human condition as such: why we are the way we are. (shrink)

In recent years, the human ability to reasoning about mental states of others in order to explain and predict their behavior has come to be a highly active area of research. Researchers from a wide range of fields { from biology and psychology through linguistics to game theory and logic{ contribute new ideas and results. This interdisciplinary workshop, collocated with the Thirteenth International Conference on Theoretical Aspects of Rationality and Knowledge (TARK XIII), aims to shed light on models of social (...) reasoning that take into account realistic resource bounds. People reason about other people's mental states in order to understand and predict the others' behavior. This capability to reason about others' knowledge, beliefs and intentions is often referred to as theory of mind. Idealized rational agents are capable of recursion in their social reasoning, and can reason about phenomena like common knowledge. Such idealized social reasoning has been modeled by modal logics such as epistemic logic and BDI (belief, desire, intention) logics and by epistemic game theory. However, in real-world situations, many people seem to lose track of such recursive social reasoning after only a few levels. The workshop provides a forum for researchers that attempt to analyze, understand and model how resource-bounded agents reason about other minds. (shrink)

The problems we deal with concern reasoning about incomplete knowledge. Knowledge is understood as ability of an ideal rational agent to make decisions about pieces of information. The formalisms we are particularly interested in are Moore's autoepistemic logic (AEL) and its variant, the logic of acceptance and rejection (AEL2). It is well-known that AEL may be seen as the nonmonotonic KD45 modal logic. The aim is to give an appropriate modal formalization for AEL2.

This edited book examines conditionals from a number of interdisciplinary perspectives, drawing on research from fields as diverse as linguistics, psychology, philosophy and logic. Across 13 chapters, the authors not only investigate and examine various commonly-held perceptions about conditionals, but they also challenge many of the assumptions underpinning current conditionals scholarship, setting an agenda for future research. Based in part on the papers presented at a unique international summer school - Conditionals in Paris - this volume represents the cutting edge (...) in the study of conditionals, and it will be of interest to scholars in fields including linguistics and psychology, semiotics, philosophy and logic, and artificial intelligence. (shrink)

Intermediate Quantitifiers presents and analyzes the logical and linguistic features of intermediate quantifiers, in a fashion typical of traditional logic. Intermediate quantifiers express logical quantities which fall between Aristotle's two quantities of categorical propositions - the universal and the particular. This book is the first to use traditional methods to integrate the logic and semantics of intermediate quantifiers with the two traditional quantities. Few, many and most express the most commonly referred to intermediate quantities, yet in this (...) book Peterson argues that an infinite number of additional quantities can be understood through a deeper examination of the logical nature of all intermediate quantifiers. Drawing on the work of Robert Carnes and taking a critical look at James McCawley's grammatical analysis, Peterson concludes that a new approach to foundations of mathematics based on the syllogistic logic of quantifiers is possible.Offering invaluable insights for those studying across areas of logic, linguistics, and the philosophy or semantics of natural language, this book presents the completion of an explanation for extending traditional syllogistic logic to handle intermediate quantifiers. (shrink)

A selection function based semantics is offered for the 'can' of ability based on the idea that 'John can run a four minute mile' is true iff John would do so under the right conditions, meaning that he would do so under at least one appropriately chosen test condition. Completeness is proved for an axiom system and semantics based on this idea, and the logic turns out to be interestingly different from any standard system of modal logic.

The basic bimodal systemK/K can be interpreted as an analysis of the logic of ability developed in [1]. Where in [1] we would express the claimI can bring it about that P using the formula, with its non-normal operator, we will now use the formula. Here is a normal alethic possibilitation operator.is a normal necessitation operator, but it is independent of, and not subject to an alethic interpretation. Rather, is interpreted to meanI bring it about that P. The result is (...) a simplification and clarification of a combined logic of ability and action like that in [2], but employing only normal operators.A number of extensions of the basic systemK/K are constructed, first by strengthening the two normal sublogics independently and then by linking the two sublogics via axiom schemata involving both operators. The result is a series of increasingly strong systems which more and more adequately fulfill our expectations for a satisfactory logic of action and ability. (shrink)

Papers presented at a workshop held during 17th-18th, January, 2008 at Technische Universit'at Berlin.

Work on 'can' in Action Theory is dichotomized into two styles of analysis: (1) what I call the indeterministic analysis, whereby for x to be able to do A means that there is no obstacle to x's doing A, and (2) the hypothetical analysis, which asserts that x is able to do A if and only if x will do A if x tries (wants, wills, chooses, etc.). This paper explores the general hypothesis that 'can' is two-ways ambiguous, that a (...) sense of opportunity corresponds to (1) and a sense of ability to something after the pattern of (2), and that a general concept of 'can' of the kind often sought after by action theorists requires a certain kind of integration of both concepts into a unified definition. The two previous most well-worked-out attempts to lay out a program along these lines, those of Sellars and Chisholm, are analyzed in detail in the hope of smoothing out some of the technical differences to provide foundations for further work of this type. An attempt is made to integrate the program with some recent developments in the concept of ability in the social sciences. The applicability of this work to some very vexing and significant problems in the social sciences is suggested. (shrink)

Different disciplines converge to trace language evolution from motor skills. The human ability to use tools has been advocated as a fundamental step toward the emergence of linguistic processes in the brain. Neuropsychological and neuroimaging research has established that linguistic functions and tool-use are mediated by partially overlapping brain networks. Yet, scholars still theoretically debate whether the relationship between tool-use and language is contingent or functionally relevant, since empirical evidence is critically missing. Here, we measured both linguistic (...) production and tool-use abilities in the same participants, as well as manual and linguistic motor skills. A path analysis ruling out unspecific contributions from manual or linguistic motor skills, showed that motor proficiency using a tool lawfully predicts differences in individual linguistic production. In addition, more complex tool-use reveals stronger association between linguistic production and tool mastery. These findings establish the existence of shared cognitive processes between tool-use and language. (shrink)

Kant ascribes two radically different kinds of language—symbolic or pictorial (qua intuitive) and discursive languages—to the “Oriental” and “Occidental” peoples respectively. By his analysis, having a merely symbolic language suggests that the “Orientals” lack understanding—and hence the ability to form concepts and think in abstracto—as well as genius and spirit. Meanwhile, he establishes discursive language as a sine qua non of the continued progress of humanity, primarily because only by means of words—as opposed to symbols—can one think (not just intuit), (...) signify one’s thoughts exactly, and make them universally communicable. Without such a language, one would not be able to make one’s feelings moral or develop a true moral character. In short, humanity would not be able to obtain its cultural or moral ends without discursive language. -/- These points add up to an exclusionary view of progress according to which the Occidental whites alone are equipped with the requisite discursive skills and other talents (including genius and spirit) to accomplish advanced culture and pursue humanity’s moral destiny. The “Orient,” with its “childish language,” is consigned to the childhood of humanity. In holding this view, Kant has departed from some of his predecessors—such as Leibniz, whose vision of the future of humanity includes an East-West harmony facilitated by a “universal symbolism,” and Rousseau, who exalts a livelier connection with the world mediated by a pictorial language. -/- The contrast with Leibniz and Rousseau also suggests that we cannot chalk up Kant’s exclusionary view of progress to mere personal prejudices. His philosophy is what gives meaning to his statements about the nature of the “Oriental” language. That is, the exclusionary view of progress emerges only when we take into account his anti-Leibnizian conceptualization of symbolic language as merely intuitive, his view that humanity is teleologically oriented toward the unique sort of moralization that he envisioned in the Groundwork, and his view that reason must lead the way in humanity’s progress toward this supposed moral end, wherefore only discursive language can facilitate such progress. (shrink)

Grodzinsky's Tree-Pruning Hypothesis can be extended to explain agrammatic comprehension disorders. Although agrammatism is evidence for syntactic modularity, there is no evidence for its anatomical modularity or for its localization in the frontal lobe. Agrammatism results from diffuse left hemisphere damage – allowing the emergence of the limited right hemisphere linguistic competence – rather than from damage to an anatomic module in the left hemisphere.