In this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic ⊢ with a composition term. Then, we investigate their position into the lattice of co...

We prove some embedding theorems for classical conditional logic, covering 'finitely cumulative' logics, 'preferential' logics and what we call 'semi-monotonic' logics. Technical tools called 'partial frames' and 'frame morphisms' in the context of neighborhood semantics are used in the proof.

Only propositional logics are at issue here. Such a logic is contra-classical in a superficial sense if it is not a sublogic of classical logic, and in a deeper sense, if there is no way of translating its connectives, the result of which translation gives a sublogic of classical logic. After some motivating examples, we investigate the incidence of contra-classicality (in the deeper sense) in various logical frameworks. In Sections 3 and 4 we will encounter, originally as an (...) example of what (in Section 2) we call a contra-classical modal logic, an unusual logic boasting a connective (" demi-negation" ) whose double application is equivalent to a single application of the negation connective. Pondering the example points the way to a general characterization of contra-classicality (Theorems 3.3 and 4.6). In an Appendix (Section 5), we look at one alternative to classical logic as the target for such translational assimilation, intuitionistic logic, calling logics which resist the assimilation, in this case, contra- intuitionistic. We will show that one such logic is classical logic itself, thereby strengthening a result of Wojcicki's to the effect that the consequence relation of classical logic cannot be faithfully embedded by any connective-by-connective translation into that of intuitionistic logic. (What the "faithfully" means here is that not only is the translation of anything provable in the 'source' logic.. (shrink)

Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result (...) of the paper, we give a very simple proof of a related but strictly stronger result. (shrink)

Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic (...) of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions. (shrink)

The main project of this dissertation is to analyze various temporal conceptions of modality for discrete n-dimensional spacetime. The first chapter contains an introduction to the problem and known results. Chapter 2 consists of a study of logics which are analogues of the so-called 'logic of today and tomorrow' and 'logic of tomorrow' investigated by Segerberg and others. We consider the analogues of these successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages and prove completeness (...) theorems. We also establish that the irreflexive successor logic in the "standard" modal language is not finitely axiomatizable. ;Chapter 3 investigates the axiomatization problem for 2-dimensional integral spacetime frames with Robb's irreflexive 'after' relation. We provide an axiomatization in a multimodal language and prove that this axiomatization is complete. We use this result to prove the system in the "standard" modal language is decidable. ;In Chapter 4 we take up the problem of what the correct Diodorean modal logic is for 2-dimensional integral spacetime. We show that the corresponding Diodorean modal logic is not S4.2, nor indeed any known modal system. We then present several candidate axioms and prove their independence in the context of S4.2. We also study some of the sublogics of the Diodorean modal logic for 2-dimensional discrete spacetime . ;The final chapter contains some general results. First we prove that for every n ≥ 2 the n-dimensional frame determines a unique Diodorean modal logic. We also consider temporal logics in the language with F and P for two kinds of irreflexive spacetime frames. We prove that for every n ≥ 2 the n-dimensional frame with Robb's 'after' relation determines a unique temporal logic. We also prove a generalized completeness theorem for n-dimensional irreflexive successor logics. Finally, in an appendix, we provide a list of selected open problems and indicate directions for future research in this area. (shrink)

We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 (...) we show that for the pure logic of one of these implicational connectives two – in general distinct – consequence relations (global and local) definable in the Kripke semantics for modal logic turn out to coincide, though this is not so for the pure logic of the other connective, and that there is an intimate relation between formulas constructed by means of the former connective and the local consequence relation. (Corollary 5.8. This, as we show in an Appendix, is connected to the fact that the ‘propositional operations’ associated with both of our implicational connectives are close to being what R. Quackenbush has called pattern functions.) Between these discussions Section 4 examines some of the replacement-of-equivalents properties of the two connectives, relative to these consequence relations, and Section 6 closes with some observations about the metaphor of identical twins as applied to such pairs of connectives. (shrink)

This paper is concerned with removing the identity schema from the axiomatic basis of deontic conditionals. This is in order to allow a stipulated ideal to be contrary or opposite in nature to the fact it is predicated upon. It is desirable, or so it is argued, to retain the order-theoretic orientation of preferential semantics towards the analysis of deontic conditionals, more specifically of maximality semantics in the tradition from Bengt Hansson. So understood, the problem involves abstracting away the settledness (...) assumption that is built in to maximality semantics. This is the assumption that what is optimal given ϕ is that which all the best ϕ-states have in common, notably ϕ itself. We propose a solution based on a strict and finite preference relation over which deontic conditionals are evaluated by letting ϕ-states evolve freely, as fate or fortune would have it, into different possibly ensuing optima that may but need not be ϕ-states themselves. The result is a deontic conditional that does not have identity. This new conditional is shown to be a proper generalization of the Hansson conditional. Hansson’s conditional can be recovered in the new idiom as a special case. Indeed, the new semantics is general enough to cover several apparently very different conceptions of deontic conditionality. For instance, the input/output logic known as basic output is a sublogic of the new system. This is somewhat surprising and suggests that there may yet be unity to be had in the field of deontic logic. (shrink)

A generalized inclusion frame consists of a set of points W and an assignment of a binary relation $R\sb{w}$ on W to each point w in W. Generalized inclusion frames whose $R\sb{w}$ are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator $>$ on comparison frames according to the following truth condition: $\alpha > \beta$ "holds at w" iff (...) every point in the truth set of $\alpha$ bears $R\sb{w}$ to some point where $\beta$ holds. ;In this essay I provide a relational frame theory which embraces both accessibility semantics and g.i. semantics as special cases. This goal is achieved via a philosophically significant generalization of universal strict implication which does not assume accessibility as a primitive. Within this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model constructions are developed which allow uniform completeness proofs for important sublogics of Lewis' V. (shrink)

We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 (...) we show that for the pure logic of one of these implicational connectives two-in general distinct-consequence relations (global and local) definable in the Kripke semantics for modal logic turn out to coincide, though this is not so for the pure logic of the other connective, and that there is an intimate relation between formulas constructed by means of the former connective and the local consequence relation. (Corollary 5.8. This, as we show in an Appendix, is connected to the fact that the 'propositional operations' associated with both of our implicational connectives are close to being what R. Quackenbush has called pattern functions.) Between these discussions Section 4 examines some of the replacement-of-equivalents properties of the two connectives, relative to these consequence relations, and Section 6 closes with some observations about the metaphor of identical twins as applied to such pairs of connectives. (shrink)

In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality , where is any natural number . The basic idea in the proof is to apply the notion (...) of companions to stit sentences in finding busy choice sequences in structures, and to make use of a relation between chains of busy choice sequences and generalized refref conditionals in connecting the two conditions of uncompactness mentioned above. (shrink)

We study interpolation properties for Shavrukov’s bimodal logic \(\textbf{GR}\) of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic \(\textbf{GR}^\circ \) of \(\textbf{GR}\) and its relational semantics. Based on our new semantics, we prove that \(\textbf{GR}^\circ \) and \(\textbf{GR}\) enjoy Lyndon interpolation property and uniform interpolation property. As a consequence of our proofs, we obtain the completeness and the finite frame property of \(\textbf{GR}^\circ \) and \(\textbf{GR}\) with respect to our new semantics.

n + 1 nested k-ary fixed point operators are more expressive than n. This holds on finite structures for all sublogics of partial fixed point logic PFP that can express conjunction, existential quantification and deterministic transitive closure of binary relations using at most k-ary fixed point operators and that are closed against subformulas. Among those are a lot of popular fixed point logics.

Barbarism was by no means unique to the past 100 years, Jonathan Glover tells us, but ''it is still right that much of 20th-century history has been a very unpleasant surprise.'' This was the century of Passchendaele, Dresden, Nanking, Nagasaki and Rwanda; of the Final Solution, the gulag, the Great Leap Forward, Year Zero and ethnic cleansing -- names that stand for killings in the six and seven figures and for suffering beyond comprehension. The technological progress that inspired the optimism (...) of the Victorians turned out also to multiply the effects of old-fashioned evil and criminal stupidity. (shrink)

The philosophies of education serve as the guide of the teachers in handling the teaching-learning process. However, a belief will remain as a belief unless it is practiced. This study aimed to find the relationship between the philosophical beliefs and practices of the 30 teachers of the schools in San Roque, Mabini, Bohol - San Roque Elementary School and San Roque National High School, S.Y. 2019-2020. The study utilized a quantitative method descriptive survey research design. The research instrument used was (...) a self-constructed questionnaire in which the reliability was tested by a Cronbach’s Alpha using Statistical Package for the Social Science (SPSS) software. Simple percentage and weighted mean were some of the statistical treatments used. Kendall’s tau_b, a non-parametric test, was used to determine the correlation between philosophical beliefs and their equivalent pedagogical practices. All of the statistical treatments were also run using the SPSS software. Further, the researcher assured the proper observation of the research ethics protocol. Based on the results, the philosophies of Progressivism (3.63) and Perennialism (3.31) were the most and least prevailing philosophical beliefs, respectively. On the other hand, the most and least prevailing philosophies practiced are Progressivism (3.69) and Essentialism (3.19), respectively. Moreover, research findings revealed that there was a significant relationship between the philosophical beliefs of teachers and their pedagogical practices. In conclusion, this study claims that teachers’ pedagogical practices are dependent to their philosophical beliefs; and as the teachers believed on a particular philosophy of education, they practice it accordingly to the extent of their adherence to the belief. (shrink)

Background: Recent research has demonstrated that depressed individuals show impairments in inhibiting irrelevant emotional material, and that these impairments are linked to rumination. Cognitive inhibition, however, is not a unitary construct but consists of several components which operate at different stages of information processing. The present study was designed to assess two components of inhibition and examine their relation to depression and rumination in a sample of clinically depressed and healthy control participants. Methods: Twenty-two individuals diagnosed with a current (...) depressive episode and 27 never-disordered control participants completed an Emotional Flanker Task to assess individual differences in interference control and a modification of the Working Memory Selection Task to assess individual differences in the ability to discard no longer relevant emotional material from working memory. Participants completed self-report measures to assess depressive symptoms and rumination. Results: Clinically depressed compared to control participants showed significantly reduced interference control of irrelevant negative information. The groups, however, did not differ in their ability to discard no longer relevant negative information from working memory. In contrast, rumination was associated with difficulty removing no longer relevant negative material from working memory but not with deficits in interference control. Conclusions: Results highlight the importance of differentiating among components of inhibition to gain a better understanding of cognitive mechanisms underlying depression and rumination. (shrink)

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close (...) by briefly discussing a general conception of conditionality that may unify the three given conceptions. (shrink)

This article integrates arguments and evidence from my 2019 monograph Heart to Heart: How Your Emotions Affect Other People. The central claim is that emotions operate as processes of relation alignment that produce convergence, complementarity, or conflict between two or more people’s orientations to objects. In some cases, relation alignment involves strategic presentation of emotional information for the purpose of regulating other people’s behaviour. In other cases, emotions consolidate from socially distributed reciprocal adjustments of cues, signals, and emerging (...) actions without any explicit registration or communication of emotional meaning by parties to the exchange. The relation-alignment approach provides a fresh perspective on issues relating to emotion’s interpersonal, intragroup, and organizational functions and clarifies how emotions are regulated for social purposes. (shrink)

Historians of science have pointed to essentialist beliefs about species as major impediments to the discovery of natural selection. The present study investigated whether such beliefs are impediments to learning this concept as well. Participants (43 children aged 4–9 and 34 adults) were asked to judge the variability of various behavioral and anatomical properties across different members of the same species. Adults who accepted within‐species variation—both actual and potential—were significantly more likely to demonstrate a selection‐based understanding of evolution than adults (...) who denied within‐species variation. The latter demonstrated an alternative, incorrect understanding of evolution and produced response patterns that were both quantitatively and qualitatively similar to those produced by preschool‐aged children. Overall, it is argued that psychological essentialism, although a useful bias for drawing species‐wide inductions, leads individuals to devalue within‐species variation and, consequently, to fail to understand natural selection. (shrink)

The article aims to show that Peirce, after realizing the appropriation that James and others made of Pragmatism, taking it far from an ideal of justice and keeping it in the service of a “nauseating utility”, whose principle was that only individual utility, including spiritual well-being, would be the ultimate goal of all practice, he sought a philosophy that would keep logic and science united in a realistic manner with laws that could be metaphysically real. In this way, he perceived (...) the necessity to transcend the hypothetical considerations incorporated into the sense of the pragmatic maxim, attempting to distance it from nominalist risk. In this process, he took into account two new normative sciences, esthetics and ethics, in addition to logic, so that Pragmaticism, in intelligent criticism, would investigate whether an admirable end of a subject could be pursued in an indefinite and prolonged course of action, without grounding it solely on individual utility, thus replacing the ideal of justice for the renamed Pragmatism, the Pragmaticism. (shrink)