A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.

Exceptional or just well connected? Political entrepreneurs and brokers in policy making

Policy brokers and policy entrepreneurs are assumed to have a decisive impact on policy outcomes. Their access to social and political resources is contingent on their influence on other agents. In social network analysis (SNA), entrepreneurs are often closely associated with brokers, because both are agents presumed to benefit from bridging structural holes; for example, gaining advantage through occupying a strategic position in relational space. Our aim here is twofold. First, to conceptually and operationally differentiate policy brokers from policy entrepreneurs premised on assumptions in the policy-process literature; and second, via SNA, to use the output of core algorithms in a cross-sectional analysis of political brokerage and political entrepreneurship. We attempt to simplify the use of graph algebra in answering questions relevant to policy analysis by placing each algorithm within its theoretical context. In the methodology employed, we first identify actors and graph their relations of influence within a specific policy event; then we select the most central actors; and compare their rank in a series of statistics that capture different aspects of their network advantage. We examine betweenness centrality, positive and negative Bonacich power, Burt’s effective size and constraint and honest brokerage as paradigmatic. We employ two case studies to demonstrate the advantages and limitations of each algorithm for differentiating between brokers and entrepreneurs: one on Swiss climate policy and one on EU competition and transport policy.

Algebra of Classical Theoretical Term Reductions in the Sciences

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type.

Relational Memory Is Evident in Eye Movement Behavior despite the Use of Subliminal Testing Methods

While it is generally agreed that perception can occur without awareness, there continues to be debate about the type of representational content that is accessible when awareness is minimized or eliminated. Most investigations that have addressed this issue evaluate access to well-learned representations. Far fewer studies have evaluated whether or not associations encountered just once prior to testing might also be accessed and influence behavior. Here, eye movements were used to examine whether or not memory for studied relationships is evident following the presentation of subliminal cues. Participants (assigned to experimental or control groups) studied scene-face pairs and test trials evaluated implicit and explicit memory for these pairs. Each test trial began with a subliminal scene cue, followed by three visible studied faces. For experimental group participants, one face was the studied associate of the scene (implicit test); for controls none were a match. Subsequently, the Display containing a match was presented to both groups, but now it was preceded by a visible scene cue (explicit test). Eye movements were recorded and recognition Memory responses were made. Participants in the experimental group looked disproportionately at matching faces on implicit test trials and participants from both groups looked disproportionately at matching faces on explicit test trials, even when that face had not been successfully identified as the associate. Critically, implicit memory-based viewing effects seemed not to depend on residual awareness of subliminal scenes cues, as subjective and objective measures indicated that scenes were successfully masked from view. The reported outcomes indicate that memory for studied relationships can be expressed in eye movement behavior without awareness.

Intracranial EEG correlates of implicit relational inference within the hippocampus

Drawing inferences from past experiences enables adaptive behavior in future situations. Inference has been shown to depend on hippocampal processes. Usually, inference is considered a deliberate and effortful mental act which happens during retrieval, and requires the focus of our awareness. Recent fMRI studies hint at the possibility that some forms of hippocampus-dependent inference can also occur during encoding and possibly also outside of awareness. Here, we sought to further explore the feasibility of hippocampal implicit inference, and specifically address the temporal evolution of implicit inference using intracranial EEG. Presurgical epilepsy patients with hippocampal depth electrodes viewed a sequence of word pairs, and judged the semantic fit between two words in each pair. Some of the word pairs entailed a common word (e.g.,‘winter - red’, ‘red - cat’) such that an indirect relation was established in following word pairs (e.g, ‘winter - cat’). The behavioral results suggested that drawing inference implicitly from past experience is feasible because indirect relations seemed to foster ‘fit’ judgments while the absence of indirect relations fostered 'do not fit' judgments, even though the participants were unaware of the indirect relations. A event-related potential (ERP) difference emerging 400 ms post-stimulus was evident in the hippocampus during encoding, suggesting that indirect relations were already established automatically during encoding of the overlapping word pairs. Further ERP differences emerged later post-stimulus (1500 ms), were modulated by the participants' responses and were evident during encoding and test. Furthermore, response-locked ERP effects were evident at test. These ERP effects could hence be a correlate of the interaction of implicit memory with decision-making. Together, the data map out a time-course in which the hippocampus automatically integrates memories from discrete but related episodes to implicitly influence future decision making.