Blockage Contraction

Blockage contraction is an operation of belief contraction that acts directly on the outcome set, i.e. the set of logically closed subsets of the original belief set K that are potential contraction outcomes. Blocking is represented by a binary relation on the outcome set. If a potential outcome X blocks another potential outcome Y, and X does not imply the sentence p to be contracted, then Y?≠?K ÷ p. The contraction outcome K ÷ p is equal to the (unique) inclusion-maximal unblocked element of the outcome set that does not imply p. Conditions on the blocking relation are specified that ensure the existence of such a unique inclusion-maximal set for all sentences p. Blockage contraction is axiomatically characterized and its relations to AGM-style operations are investigated. In a finite-based framework, every transitively relational partial meet contraction is also a blockage contraction.     

Theories with the Independence Property

A first-order theory T{{\mathcal T}} has the Independence Property provided T   \vdash (Q)(FT F₁ ú. . .úF_n){{{\mathcal T} \, \, \vdash (Q)(\Phi \Rightarrow {\Phi_1} \vee.\,.\,.\vee {\Phi_n})}} implies T   \vdash (Q)(FT F_i){{{\mathcal T} \, \, \vdash (Q)(\Phi \Rightarrow {\Phi_i})}} for some i whenever F,F₁, . . . ,F_n{{\Phi,\Phi_1,\,.\,.\,.\,,\Phi_n}} are formulae of a suitable type and (Q) is any quantifier sequence. Variants of this property have been noticed for some time in logic programming and in linear programming.     

Belief contraction without recovery

The postulate of recovery is commonly regarded to be the intuitively least compelling of the six basic Gärdenfors postulates for belief contraction. We replace recovery by the seemingly much weaker postulate of core-retainment, which ensures that if x is excluded from K when p is contracted, then x plays some role for the fact that K implies p. Surprisingly enough, core-retainment together with four of the other Gärdenfors postulates implies recovery for logically closed belief sets. Reasonable contraction operators without recovery do not seem to be possible for such sets. Instead, however, they can be obtained for non-closed belief bases. Some results on partial meet contractions on belief bases are given, including an axiomatic characterization and a non-vacuous extension of the AGM closure condition.     

System of Spheres-based Multiple Contractions

We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the partial meet multiple contractions.     

Examining the role of lexical frequency in the acquisition and processing of sentential complements

We present empirical data showing that the relative frequency with which a verb normally appears in a syntactic construction predicts young children's ability to remember and repeat sentences instantiating that construction. Children aged 2;10–5;8 years were asked to repeat grammatical and ungrammatical sentential complement sentences (e.g., ‘I think + S’). The sentences contained complement-taking verbs (CTVs) used with differing frequencies in children's natural speech. All children repeated sentences containing high frequency CTVs (e.g., think) more accurately than those containing low frequency CTVs (e.g., hear), and made more sophisticated corrections to ungrammatical sentences containing high frequency CTVs. The data suggest that, like adults, children are sensitive to lexico-constructional collocations. The implications for language acquisition are discussed.     

The Geometry of Enhancement in Multiple Regression

In linear multiple regression, “enhancement” is said to occur when R ²=b′r>r′r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R _xx≠I, R _xx=E[xx′]=V Λ V′ (where V Λ V′ denotes the eigen decomposition of R _xx; λ ₁>λ ₂), the set B₁:={b_i:R²=b_i￠r_i=r_i￠r_i;0 < R² ￡ 1}\boldsymbol{B}_{1}:=\{\boldsymbol{b}_{i}:R^{2}=\boldsymbol{b}_{i}'\boldsymbol{r}_{i}=\boldsymbol{r}_{i}'\boldsymbol{r}_{i};0R² ￡ 1;R²l_p ￡ r_i￠r_i < R²}0p≥3 (and λ ₁>λ ₂>⋯>λ _p ), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B ₁ occurs at the intersection of two hyper-ellipsoids in ℝ ^p . Equations are provided for populating the sets B ₁ and B ₂ and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ _p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included in Appendices A and B.     

A kinematic and dynamic comparison of surface and underwater displacement in high level monofin swimming

Fin swimming performance can be divided into underwater and surface water races. World records are about 10% faster for underwater swimming vs. surface swimming, but little is known about the advantage of underwater swimming for monofin swimming. Some authors reported that the air–water interface influences the kinematics and leads to a narrow vertical amplitude of the fin. On the one hand, surface swimming is expected to affect drag parameters (cross-sectional area (S) and active drag (AD)) when compared to underwater swimming. On the other hand, the surface swimming technique may also affect efficiency (η_F). The aim of this study is therefore to evaluate and compare drag parameters and efficiency during underwater and surface swimming. To this end, 12 international level monofin swimmers were measured during both underwater and surface swimming. Kinematic parameters (both dimensional and non-dimensional), η_F (calculated according to the Elongated-Body Theory), and AD (computed with Velocity Perturbation Method) were calculated for an underwater and a surface fin swimming trial, performed at maximal speed. As expected, results showed significantly lower velocities during surface swimming vs. underwater  = 2.5 m s⁻¹ vs.  = 2.36 m s⁻¹, p < .01). Velocities during underwater and surface swimming were strongly correlated (r = .97, p < .01). Underwater swimming was also associated with higher vertical amplitudes of the fin compared to surface swimming ( = 0.55 m vs. ) = 0.46 m, p < .01). Length-specific amplitudes (A_under/L_b) were in the order of 20% during underwater swimming as for undulating fish, and significantly higher than during surface swimming (A_surf/L_b = 17%, p < .01). Efficiency for surface swimming was about 6% lower than for underwater swimming ( = 0.79 vs.  = 0.74, p < .01). This decrease could be associated with an increase in swimming frequency for surface swimming ( = 2.15 Hz vs.  = 2.08 Hz, p < .01). Active drag during surface swimming was about 7% higher than for underwater swimming ( = 78.9 N vs.  = 84.7 N, p < .01). A significantly smaller cross-sectional area for surface swimming ( = 0.053 m² vs.  = 0.044 m², p < .01) and higher drag coefficient for surface swimming ( = 0.47 vs.  = 0.69, p < .01) were measured. Finally, correlation between cross-sectional area and vertical amplitude of the fin was reported for both underwater and surface swimming. These results suggest that the performance improvement during underwater swimming is not only linked to a wave drag reduction effect but also to a specific swimming technique due to the free surface.     

Students' defending and passive bystanding behaviours when witnessing school bullying in North Western Ethiopia: Roles of personal and situational factors

Guided by Thornberg et al.'s (2012) framework on motivation to intervene, the present study examines whether personal and situational factors are associated with defending and passive bystanding behaviours in school bullying. Self-reported survey data were collected from 612 students (aged 12–16 years) attending grades 7, 8, 9, and 10 in East Gojjam Administrative Zone, North Western Ethiopia. Hierarchical regression analysis revealed that the strongest, significant predictors of defending were self-efficacy for defending (β = .215, p = .000), affective empathy (β = .173, p = .000), students' experience as victim (β = .119, p = .002), personal sense of power (β = .119, p = .006), followed by moral disengagement (β = .118, p = .002), and age level (β = −.082, p = .036). All variables jointly explained 18.6% of the total variance in defending, F (12, 599) = 11.397, p < .00; with medium effect size (f² = 0.23). In contrast, the strongest predictors of passive bystanding were moral disengagement (β = .233, p = .000), perceived costs and benefits of defending (β = −.163, p = .000), self-efficacy (β = −.139, p = .003), students' experience as victim (β = .097, p = .014), followed by gender (β = −.080, p = .042). The model explained 16.7% of the total variance in passive bystanding, F (12, 599) = 10.043, p < .001; with medium effect size (f² = 0.20). The findings enrich our understanding of factors associated with defending and passive bystanding behaviours. The implications for intervention are discussed. Please refer to the Supplementary Material section to find this article's Community and Social Impact Statement.     

Bootstrap Contraction

We can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious candidate that can be the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction.     

New Foundations for a Relational Theory of Theory-revision

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions ‘J is a contraction of K with respect to A’ and ‘J is a revision of K with respect to A’. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for AGM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions?     

Shared structuring resources across domains: double task effects from linguistic processing on the structural integration of pitch sequences

Many studies have reported evidence suggesting that resources involved in linguistic structural processing might be domain-general by demonstrating interference from simultaneously presented non-linguistic stimuli on the processing of sentences (Slevc, Rosenberg, & Patel, 2009 Slevc, L. R., Rosenberg, J. C., & Patel, A. D. (2009). Making psycholinguistics musical: Self-paced reading time evidence for shared processing of linguistic and musical syntax. Psychonomic Bulletin & Review, 16(2), 374–381. doi:10.3758/16.2.374[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). However, the complexity of the analysed linguistic processes often precludes the interpretation of such interference as being based on structural—rather than more general—processing resources (Perruchet & Poulin-Charronnat, 2013 Perruchet, P., & Poulin-Charronnat, B. (2013). Challenging prior evidence for a shared syntactic processor for language and music. Psychonomic Bulletin & Review, 20(2), 310–317. doi:10.3758/s13423-012-0344-5[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). We therefore used linguistic structure as a source of interference for another structural processing task, by asking participants to read sentences while processing experimentally manipulated pitch sequences. Half of the sentences contained a segment with either an “out-of-context” sentential violation or a “garden path” unexpectancy. Furthermore, the pitch sequences contained a cluster shift, which did or did not align with the sentential unexpectancies. A two-tone recognition task followed each pitch sequence, providing an index of the strength with which this structural boundary was processed. When a “garden path” unexpectancy (requiring structural reintegration) accompanied the cluster shift, the structural boundary induced by this shift was processed more shallowly. No such effect occurred with non-reintegratable “out-of-context” sentential violations. Furthermore, the discussed interference effect can be isolated from general pitch recognition performance, supporting the interpretation of such interference as being based on overlapping structural processing resources (Kljajevic, 2010 Kljajevic, V. (2010). Is syntactic working memory language specific? Psihologija, 43(1), 85–101. doi:10.2298/PSI1001085K[Crossref], [Web of Science ®] , [Google Scholar]; Patel, 2003 Patel, A. D. (2003). Language, music, syntax and the brain. Nature Neuroscience, 6(7), 674–681. doi: 10.1038/nn1082[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]).     

The adequacy of the theories of deductive systems with respect to sentential calculi

Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS _r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS _r , the variablesX, Y, Z ... represent the subsets ofS _R . The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS _R δ(X) means, thatX is closed with respect to the modus ponens rule.A _R designates the class of allS _R -substitutions of the axioms of the sentential calculusR.     

On the Modal Definability of Simulability by Finite Transitive Models

We show that given a finite, transitive and reflexive Kripke model 〈 W, ≼, ⟦ ⋅ ⟧ 〉 and w ? W{w \in W} , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bisimulation is definable in the standard modal language even over the class of K4 models, a fairly standard result for which we also provide a proof.     

On the dynamics of institutional agreements

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form A_G:x j{\rm A}_{G:x} \varphi reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that j{\varphi} ’. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!y{x!\psi}, meaning that the agents learn that y{\psi} is the case in context x. Formulae of the form [x!y]j{[x!\psi]\varphi} mean that j{\varphi} is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all \lnoty{\lnot\psi} -worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form G:x-y{G:x\uparrow\psi}. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called ‘doctrinal paradox’ or ‘discursive dilemma’ (Pettit, Philosophical Issues 11:268–299, 2001; Kornhauser and Sager, Yale Law Journal 96:82–117, 1986).     

Non‐Classical Knowledge

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely‐held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single‐premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker‐than‐classical K₃ logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to—whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non‐classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities.     

Algebraic aspects of deduction theorems

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian.A part of this paper was presented in abstracted form in Bulletin of the Section of Logic, Vol. 12, No. 3 (1983), pp. 111–116, and in The Journal of Symbolic Logic.