An observation on Carnapʼs Continuum and stochastic independencies

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson?s Sufficientness Principle holds, thus giving Carnap?s Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap?s Continuum for the language with just a single predicate.     

Methodological naturalism and epistemic internalism

Epistemic naturalism holds that the results or methodologies from the cognitive sciences are relevant to epistemology, and some have maintained that scientific methods are more compatible with externalist theories of justification than with internalist theories. But practically all discussions about naturalized epistemology are framed exclusively in terms of cognitive psychology, which is only one of the cognitive sciences. The question addressed in this essay is whether a commitment to naturalism really does favor externalism over internalism, and we offer reasons for thinking that naturalism in epistemology is compatible with both internalist and externalist conceptions of justification. We also argue that there are some distinctively internalist aims that are currently being studied scientifically and these notions, and others, should be studied by scientific methods. This essay is dedicated to Deborah Mayo, who has long advocated using error statistical techniques to analyze and resolve epistemological puzzles in the philosophy of science. This essay follows the same spirit by advocating that computational concepts and techniques be applied within the heart of traditional, analytic epistemology.     

The logic, intentionality, and phenomenology of emotion

My concern in this paper is with the intentionality of emotions. Desires and cognitions are the traditional paradigm cases of intentional attitudes, and one very direct approach to the question of the intentionality of emotions is to treat it as sui generis—as on a par with the intentionality of desires and cognitions but in no way reducible to it. A more common approach seeks to reduce the intentionality of emotions to the intentionality of familiar intentional attitudes like desires and cognitions. In this paper, I argue for the sui generis approach.

An ERP investigation of conditional reasoning with emotional and neutral contents

In two experiments we investigate conditional reasoning using event-related potentials (ERPs). Our goal was to examine the time course of inference making in two conditional forms, one logically valid (Modus Ponens, MP) and one logically invalid (Affirming the Consequent, AC). We focus particularly on the involvement of semantically-based inferential processes potentially marked by modulations of the N400. We also compared reasoning about emotional and neutral contents with separate sets of stimuli of differing linguistic complexity across the two experiments. Both MP and AC modulated the N400 component, suggesting the involvement of a semantically-based inferential mechanism common across different logical forms, content types, and linguistic features of the problems. Emotion did not have an effect on early components, and did not interact with components related to inference making. There was a main effect of emotion in the 800–1050 ms time window, consistent with an effect on sustained attention. The results suggest that conditional reasoning is not a purely formal process but that it importantly implicates semantic processing, and that the effect of emotion on reasoning does not primarily operate through a modulation of early automatic stages of information processing.     

Rule-based schema matching for ontology-based mediators

Mediating heterogeneous data sources heavily relies on explicit domain knowledge expressed, for example, as ontologies and mapping rules. We discuss the use of logic representations for mapping schema elements onto concepts expressed in a simplified ontology for cultural assets. Starting with a logic representation of the ontology, criteria for a rule-based schema matching are exemplified. Special requirements are the handling of uncertain information and the processing of hierarchical XML structures representing instances.     

Epistemology and artificial intelligence

In this essay we advance the view that analytical epistemology and artificial intelligence are complementary disciplines. Both fields study epistemic relations, but whereas artificial intelligence approaches this subject from the perspective of understanding formal and computational properties of frameworks purporting to model some epistemic relation or other, traditional epistemology approaches the subject from the perspective of understanding the properties of epistemic relations in terms of their conceptual properties. We argue that these two practices should not be conducted in isolation. We illustrate this point by discussing how to represent a class of inference forms found in standard inferential statistics. This class of inference forms is interesting because its members share two properties that are common to epistemic relations, namely defeasibility and paraconsistency. Our modeling of standard inferential statistical arguments exploits results from both logical artificial intelligence and analytical epistemology. We remark how our approach to this modeling problem may be generalized to an interdisciplinary approach to the study of epistemic relations.     

Logic programs and connectionist networks

One facet of the question of integration of Logic and Connectionist Systems, and how these can complement each other, concerns the points of contact, in terms of semantics, between neural networks and logic programs. In this paper, we show that certain semantic operators for propositional logic programs can be computed by feedforward connectionist networks, and that the same semantic operators for first-order normal logic programs can be approximated by feedforward connectionist networks. Turning the networks into recurrent ones allows one also to approximate the models associated with the semantic operators. Our methods depend on a well-known theorem of Funahashi, and necessitate the study of when Funahashi's theorem can be applied, and also the study of what means of approximation are appropriate and significant.     

Proof theory and mathematical meaning of paraconsistent C-systems

A proof-theoretic analysis and new arithmetical semantics are proposed for some paraconsistent C-systems, which are a relevant sub-class of Logics of Formal Inconsistency (LFIs) introduced by W.A. Carnielli et al. (2002, 2005) [8] and [9]. The sequent versions BC, CI, CIL of the systems bC, Ci, Cil presented in Carnielli et al. (2002, 2005) [8] and [9] are introduced and examined. BC, CI, CIL admit the cut-elimination property and, in general, a weakened sub-formula property. Moreover, a formal notion of constructive paraconsistent system is given, and the constructivity of CI is proven. Further possible developments of proof theory and provability logic of CI-based arithmetical systems are sketched, and a possible weakened Hilbert?s program is discussed. As to the semantical aspects, arithmetical semantics interprets C-system formulas into Provability Logic sentences of classical Arithmetic PA (Artemov and Beklemishev (2004) [2], Japaridze and de Jongh (1998) [19], Gentilini (1999) [15], Smorynski (1991) [22]): thus, it links the notion of truth to the notion of provability inside a classical environment. It makes true infinitely many contradictions B∧¬B and falsifies many arbitrarily complex instances of non-contradiction principle ¬(A∧¬A). Moreover, arithmetical models falsify both classical logic LK and intuitionistic logic LJ, so that a kind of metalogical completeness property of LFI-paraconsistent logic w.r.t. arithmetical semantics is proven. As a work in progress, the possibility to interpret CI-based paraconsistent Arithmetic PACI into Provability Logic of classical Arithmetic PA is discussed, showing the role that PACIarithmetical models could have in establishing new meta-mathematical properties, e.g. in breaking classical equivalences between consistency statements and reflection principles.     

Levels of modality for BDI Logic

The use of rational agents for modelling real world problems has both been heavily investigated and become well accepted, with BDI (Beliefs, Desires, and Intentions) Logic being a widely used architecture to represent and reason about rational agency. However, in the real world, we often have to deal with different levels of confidence in the beliefs we hold, desires we have, and intentions that we commit to. This paper extends our previous framework that integrated qualitative levels of beliefs, desires, and intentions into BDI Logic. We describe an expanded set of axioms and properties of the extended logic. We present a modular structure for the semantics which involves a non-normal Kripke type semantics that may be used for other agent systems. Further, we demonstrate the usefulness of our framework with a scheduling task example.     

Justification logics and hybrid logics

Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since justification logics are newer and less well known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here.