Pure Modal Logic of Names and Tableau Systems

By a pure modal logic of names (PMLN) we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de re and which is an extension of Propositional Logic. For categorical sentences we use two interpretations: a “natural” one; and Johnson and Thomason’s interpretation, which is suitable for some reconstructions of Aristotelian modal syllogistic (Johnson in Notre Dame J Form Logic 30(2):271–284, 1989; Thomason in J Philos Logic 22(2):111–128, 1993 and J Philos Logic 26:129–141, 1997. In both cases we use Johnson-like models (1989). We also analyze different kinds of versions of PMLN, for both general and singular names. We present complete tableau systems for the different versions of PMLN. These systems enable us to present some decidability methods. It yields “strong decidability” in the following sense: for every inference starting with a finite set of premises (resp. every syllogism, every formula) we can specify a finite number of steps to check whether it is logically valid. This method gives the upper bound of the cardinality of models needed for the examination of the validity of a given inference (resp. syllogism, formula).     

Sustained increase in hippocampal sharp-wave ripple activity during slow-wave sleep after learning

High-frequency oscillations, known as sharp-wave/ripple (SPW-R) complexes occurring in hippocampus during slow-wave sleep (SWS), have been proposed to promote synaptic plasticity necessary for memory consolidation. We recorded sleep for 3 h after rats were trained on an odor-reward association task. Learning resulted in an increased number SPW-Rs during the first hour of post-learning SWS. The magnitude of ripple events and their duration were also elevated for up to 2 h after the newly formed memory. Rats that did not learn the discrimination during the training session did not show any change in SPW-Rs. Successful retrieval from remote memory was likewise accompanied by an increase in SPW-R density and magnitude, relative to the previously recorded baseline, but the effects were much shorter lasting and did not include increases in ripple duration and amplitude. A short-lasting increase of ripple activity was also observed when rats were rewarded for performing a motor component of the task only. There were no increases in ripple activity after habituation to the experimental environment. These experiments show that the characteristics of hippocampal high-frequency oscillations during SWS are affected by prior behavioral experience. Associative learning induces robust and sustained (up to 2 h) changes in several SPW-R characteristics, while after retrieval from remote memory or performance of a well-trained procedural aspect of the task, only transient changes in ripple density were induced.     

Socratic Proofs

Journal of Philosophical Logic - Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: “Is A derivable from...     

Do university students really have difficulty in duration judgments? Comment on Okazaki and Matsuda (2008, 2010)

Reinterpretation suggests that low performance of the participants studied by Okazaki and Matsuda (2008, 2010) may have been caused by using a procedure which overloads the cognitive capacities of undergraduate students. The questions asked participants about their reasoning could have led to cognitive overload because they performed two tasks: judgment of movement duration and paying attention to what kind of knowledge should be used (alpha or beta). Some interpretations are offered referring to possible effects of training procedures for applying both kinds of knowledge.     

A Method of Generating Modal Logics Defining Jaśkowski’s Discussive Logic D<Subscript>2</Subscript>

Ja?kowski’s discussive logic D₂ was formulated with the help of the modal logic S5 as follows (see [7, 8]): \({A \in {D_{2}}}\) iff \({\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}\), where (–)^? is a translation of discussive formulae from For^d into the modal language. We say that a modal logic L defines D₂ iff \({{\rm D}_{2} = \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}\). In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (?): have the same theses beginning with ‘\({\diamond}\)’ as S5. Of course, all logics fulfilling the above condition, define D₂. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D₂ is equivalent to having the property (?). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (?). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D₂.     

A Study in Grzegorczyk Point-Free Topology Part II: Spaces of Points

Studia Logica - In the second installment to Gruszczyński and Pietruszczak (Stud Log, 2018. https://doi.org/10.1007/s11225-018-9786-8 ) we carry out an analysis of spaces of points of...