Independence in Information Spaces

Three different types of interdependence between pieces of information, or ??secrets??, are discussed and compared. Two of them, functional dependence and nondeducibility, have been studied and axiomatized before. This article introduces a third type of interdependence and provides a complete and decidable axiomatization of this new relation.     

Squares in Fork Arrow Logic

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares.     

Normative naturalism and Popperian views on reduction

Eric Scerri has argued that chemists using ab initio calculations pursue a partial reduction of chemistry to physics, while accepting that full reduction (through axiomatization) is impractical. He characterizes this view as Popperian and naturalistic. However, Popper's position on reduction is not naturalistic, as he rejected axiomatization for different reasons.     

What is the axiomatic method?

The modern notion of the axiomatic method developed as a part of the conceptualization of mathematics starting in the nineteenth century. The basic idea of the method is the capture of a class of structures as the models of an axiomatic system. The mathematical study of such classes of structures is not exhausted by the derivation of theorems from the axioms but includes normally the metatheory of the axiom system. This conception of axiomatization satisfies the crucial requirement that the derivation of theorems from axioms does not produce new information in the usual sense of the term called depth information. It can produce new information in a different sense of information called surface information. It is argued in this paper that the derivation should be based on a model-theoretical relation of logical consequence rather than derivability by means of mechanical (recursive) rules. Likewise completeness must be understood by reference to a model-theoretical consequence relation. A correctly understood notion of axiomatization does not apply to purely logical theories. In the latter the only relevant kind of axiomatization amounts to recursive enumeration of logical truths. First-order “axiomatic” set theories are not genuine axiomatizations. The main reason is that their models are structures of particulars, not of sets. Axiomatization cannot usually be motivated epistemologically, but it is related to the idea of explanation.     

The Moses, mega-Moses, and Armstrong illusions: integrating language comprehension and semantic memory

This study develops a new theory of the Moses illusion, observed in responses to general knowledge questions such as, "How many animals of each kind did Moses take on the Ark?" People often respond "two" rather than "zero" despite knowing that Noah, not Moses, launched the Ark. Our theory predicted two additional types of conceptual error demonstrated here: the Armstrong and mega-Moses illusions. The Armstrong illusion involved questions resembling, "What was the famous line uttered by Louis Armstrong when he first set foot on the moon?" People usually comprehend such questions as valid, despite knowing that Louis Armstrong was a jazz musician who never visited the moon. This Armstrong illusion was not due to misperceiving the critical words (Louis Armstrong), and occurred as frequently as the Moses illusion (with critical words embedded in identical sentential contexts), but less frequently than the mega-Moses illusion caused when Moses and Armstrong factors were combined.     

On the Dynamic Logic of Agency and Action

We present a Hilbert style axiomatization and an equational theory for reasoning about actions and capabilities. We introduce two novel features in the language of propositional dynamic logic, converse as backwards modality and abstract processes specified by preconditions and effects, written as ${\varphi \Rightarrow \psi}$ and first explored in our recent paper (Hartonas, Log J IGPL Oxf Univ Press, 2012), where a Gentzen-style sequent calculus was introduced. The system has two very natural interpretations, one based on the familiar relational semantics and the other based on type semantics, where action terms are interpreted as types of actions (sets of binary relations). We show that the proof systems do not distinguish between the two kinds of semantics, by completeness arguments. Converse as backwards modality together with action types allow us to produce a new purely equational axiomatization of Dynamic Algebras, where iteration is axiomatized independently of box and where the fixpoint and Segerberg induction axioms are derivable. The system also includes capabilities operators and our results provide then a finitary Hilbert-style axiomatization and a decidable system for reasoning about agent capabilities, missing in the KARO framework.     

Syntactic priming effects in aphasia: an investigation of local syntactic dependencies

This study explored on-line processing of local syntactic dependencies in normal subjects and in Broca's and Wernicke's aphasics using a lexical decision paradigm. In addition, subjects performed a grammatically judgement task on the real word pairs used in the lexical decision tasks. Results of two experiments for normal subjects indicated different syntactic priming effects as a function of the type of local syntactic dependency. Word pairs that formed a single constituent phrase, i.e., a verb phrase, showed both facilitory and inhibitory effects, whereas word pairs that reflected local syntactic dependencies across a phrase boundary, i.e., pronoun verb, showed only inhibitory effects. Broca's aphasics failed to show facilitory effects when presented with word pairs forming a single constituent phrase but, similar to normals, did show inhibition when presented with word pairs that reflected local syntactic dependencies across a phrase boundary. In contrast, Wernicke's aphasics failed to show inhibitory effects in both experiments. The implications of these results for theories of language processing deficits in aphasia are considered.     

Armstrong on Probabilistic Laws of Nature

D. M. Armstrong famously claims that deterministic laws of nature are contingent relations between universals and that his account can also be straightforwardly extended to irreducibly probabilistic laws of nature. For the most part, philosophers have neglected to scrutinize Armstrong’s account of probabilistic laws. This is surprising precisely because his own claims about probabilistic laws make it unclear just what he takes them to be. We offer three interpretations of what Armstrong-style probabilistic laws are, and argue that all three interpretations are incompatible either with some feature of Armstrong’s broader metaphysics or with essential features of his account of laws (or both).     

ALTERNATIVE AXIOMATICS AND COMPLEXITY OF DELIBERATIVE STIT THEORIES

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT.     

Nomic Universals and Particular Causal Relations: Which are Basic and Which are Derived?

Armstrong holds that a law of nature is a certain sort of structural universal which, in turn, fixes causal relations between particular states of affairs. His claim that these nomic structural universals explain causal relations commits him to saying that such universals are irreducible, not supervenient upon the particular causal relations they fix. However, Armstrong also wants to avoid Plato’s view that a universal can exist without being instantiated, a view which he regards as incompatible with naturalism. This construal of naturalism forces Armstrong to say that universals are abstractions from a certain class of particulars; they are abstractions from first-order states of affairs, to be more precise. It is here argued that these two tendencies in Armstrong cannot be reconciled: To say that universals are abstractions from first-order states of affairs is not compatible with saying that universals fix causal relations between particulars. Causal relations are themselves states of affairs of a sort, and Armstrong’s claim that a law is a kind of structural universal is best understood as the view that any given law logically supervenes on its corresponding causal relations. The result is an inconsistency, Armstrong having to say that laws do not supervene on particular causal relations while also being committed to the view that they do so supervene. The inconsistency is perhaps best resolved by denying that universals are abstractions from states of affairs.

All Together Now: Concurrent Learning of Multiple Structures in an Artificial Language

Natural languages contain many layers of sequential structure, from the distribution of phonemes within words to the distribution of phrases within utterances. However, most research modeling language acquisition using artificial languages has focused on only one type of distributional structure at a time. In two experiments, we investigated adult learning of an artificial language that contains dependencies between both adjacent and non‐adjacent words. We found that learners rapidly acquired both types of regularities and that the strength of the adjacent statistics influenced learning of both adjacent and non‐adjacent dependencies. Additionally, though accuracy was similar for both types of structure, participants’ knowledge of the deterministic non‐adjacent dependencies was more explicit than their knowledge of the probabilistic adjacent dependencies. The results are discussed in the context of current theories of statistical learning and language acquisition.     

Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic

We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.     

Is the Humean defeated by induction?

Many necessitarians about cause and law (Armstrong, What is a law of nature. Cambridge University Press, Cambridge, 1983; Mumford, Laws in nature. Routledge Studies in Twentieth-Century Philosophy. Routledge, Abingdon, 2004; Bird, Nature’s metaphysics: Laws and properties. Oxford University Press, Oxford, 2007) have argued that Humeans are unable to justify their inductive inferences, as Humean laws are nothing but the sum of their instances. In this paper I argue against these necessitarian claims. I show that Armstrong is committed to the explanatory value of Humean laws (in the form of universally quantified statements), and that contra Armstrong, brute regularities often do have genuine explanatory value. I finish with a Humean attempt at a probabilistic justification of induction, but this fails due to its assumption that the proportionality syllogism is justified. Although this attempt fails, I nonetheless show that the Humean is at least as justified in reasoning inductively as Armstrong.     

Recycling Religion: Lance Armstrong’s Postmodern Spirituality of Suffering and Survivorship

For much of his triple career as heroic cancer survivor, sports champion, and, latterly, fallen idol, Lance Armstrong, a professed atheist, has worn a silver necklace with a cross pendant. Why does he wear this Ur-symbol of Christian religious faith? Speculative answers range from ‘residual superstition’ to ‘fashion jewellery’ and ‘tactical deception’. Here, Armstrong’s own declared beliefs as refracted through his autobiographical accounts are analysed within a mono-mythic framework, with particular emphasis on ‘survivorship’, his implicit spirituality of suffering. The Armstrong case of a personalised construction of faith praxis sheds light on the eclectic ‘liquid’ religio-spiritual style of postmodernism. It helps portray the negotiation of the religious-in-the-secular, the sacred-in-the-profane (and vice versa), and illuminates the problematic nature of dualistic accounts of religion and spirituality in contemporary culture. Armstrong’s ‘recycling’ of traditional religious iconography out of context of origin demonstrates the persistence, durability, and elasticity of religio-spiritual symbolic culture.     

Order-Independent Transformative Decision Rules

A transformative decision rule alters the representation of a decision problem, either by changing the set of alternative acts or the set of states of the world taken into consideration, or by modifying the probability or value assignments. A set of transformative decision rules is order-independent in case the order in which the rules are applied is irrelevant. The main result of this paper is an axiomatic characterization of order-independent transformative decision rules, based on a single axiom. It is shown that the proposed axiomatization resolves a problem observed by Teddy Seidenfeld in a previous axiomatization by Peterson.     

Critical bands and mixed-frequency scaling: sequential dependencies, equal-loudness contours, and power function exponents

Stimuli of random intensities and various but predictable frequencies were presented for repeated magnitude estimations on the same scale (mixed-frequency scaling). The frequencies for a particular judgment session were selected so that they lay either inside each other's critical bands or outside them. Contrastive dependencies of current magnitude estimation responses on previous stimuli of a different frequency were significantly affected by whether the two frequencies were inside or outside each other's critical bands, while assimilative dependencies were not. This reinforces the idea that such dependencies are sensory in nature and arise from a different mechanism than do the assimilative dependencies. Mixed-frequency scaling of loudness also gives rise to cross-frequency matching functions from which equal-loudness contours can be calculated. These contours calculated from the present judgments are similar to those produced from other methods, even when they are extrapolated to untested intensities. Power function exponents for loudness scaled in this way are larger for lower frequencies, as has been found in previous studies, and are consistent with the flattening of the calculated equal-loudness contours for low frequencies as intensity increases.     

Exemplification as molecular function

Since the publication of Universals and Scientific Realism (Armstrong 1978a, b) until Sketch for a Systematic Metaphysics (Armstrong 2010), via Universals: An Opinionated Introduction (Armstrong 1989), a World of States of Affairs (Armstrong 1997), and Truth and Truthmakers (Armstrong 2004), David Armstrong has developed one of the most influential theories of instantiation in contemporary analytic metaphysics (see, for example, Lewis, in Aust J Phil 61(4), 343–377, 1983; Baxter in Aust J Phil, 79, 449–464, 2001; Forrest, in Aust J Phil, 83, 213–228, 2006). Instantiation has been advocated by Armstrong to give a solution to what he has called the “pressing problem” of “the multiple location of property universals” (Armstrong, in Universals: An opinionated introduction. University Press, Cambridge, 1989, pp. 89–90). Here I argue that Armstrong’s theory of instantiation fails to solve the problem because it involves two kinds of instantiation to account for particulars “having” and “sharing” universals. As a viable alternative to Armstrong’s theory, I propose a theory of instantiation capable of accounting for both phenomena in a univocal way.     

Troubling spaces: Ecological risk,narrative framing,and emotional engagement in The Age of Stupid

Franny Armstrong’s The Age of Stupid (2009) presents itself as a documentary about ecological risk and environmental injustice in different geographical regions, while at the same time appealing strongly to our emotions by showing us something we are not yet able to see: the possibly catastrophic future consequences of our present behavior. Through the use of spatial and temporal framing, Armstrong creates a strong cognitive and affective link between the documentation of current social and environmental practices and the imagination of future ecological devastation. Drawing on the pioneering work of cognitive film theorists and other scholars interested in the emotional appeal of non-fiction film, I investigate how The Age of Stupid mediates threatened ecological spaces and associated environmental risks in order to provoke strong affective and cognitive responses from viewers and, ideally, move them to action.     

Axiomatization of a Branching Time Logic with Indistinguishability Relations

Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.