Full Lambek Hyperdoctrine: Categorical Semantics for First-Order Substructural Logics

2013 ◽  
pp. 211-225 ◽  
Author(s):  
Yoshihiro Maruyama
Keyword(s):  
Substructural Logics ◽  
First Order ◽  
Categorical Semantics

Topos-theoretic background

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Category Theory ◽  
Order Theory ◽  
Order Logic ◽  
Basic Theory ◽  
First Order Logic ◽  
Syntactic Category ◽  
First Order ◽  
Deductive Systems ◽  
First Order Theory ◽  
Categorical Semantics

This chapter provides the topos-theoretic background necessary for understanding the contents of the book; the presentation is self-contained and only assumes a basic familiarity with the language of category theory. The chapter begins by reviewing the basic theory of Grothendieck toposes, including the fundamental equivalence between geometric morphisms and flat functors. Then it presents the notion of first-order theory and the various deductive systems for fragments of first-order logic that will be considered in the course of the book, notably including that of geometric logic. Further, it discusses categorical semantics, i.e. the interpretation of first-order theories in categories possessing ‘enough’ structure. Lastly, the key concept of syntactic category of a first-order theory is reviewed; this notion will be used in Chapter 2 for constructing classifying toposes of geometric theories.

scholarly journals A Novel Categorical Approach to Semantics of Relational First-Order Logic

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1584
Author(s):  
Wolfgang Schreiner ◽  
William Steingartner ◽  
Valerie Novitzká
Keyword(s):  
Term Structure ◽  
Set Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Basic Logic ◽  
Categorical Approach ◽  
First Order ◽  
The Core ◽  
Deduction Rules ◽  
Categorical Semantics

We present a categorical formalization of a variant of first-order logic. Unlike other texts on this topic, the goal of this paper is to give a very transparent and self-contained account without requiring more background than basic logic and set theory. Our focus is to show how the semantics of first-order formulas can be derived from their usual deduction rules. For understanding the core ideas, it is not necessary to investigate the internal term structure of atomic formulas, thus we abstract atomic formulas to (syntactically opaque) relations; in this sense, our variant of first-order logic is “relational”. While the derived semantics is based on categorical principles (even the duality that arises from a symmetry between two ways of looking at something where there is no reason to choose one over the other), it is nevertheless “constructive” in that it describes explicit computations of the truth values of formulas. We demonstrate this by modeling the categorical semantics in the RISCAL (RISC Algorithm Language) system which allows us to validate the core propositions by automatically checking them in finite models.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Morphological studies of linear (AB)n multiblock copolymers and their blends

1992 ◽  
Vol 50 (1) ◽  
pp. 384-385
Author(s):  
Richard J. Spontak ◽  
Steven D. Smith ◽  
Arman Ashraf
Keyword(s):  
Electron Microscopy ◽  
Microphase Separation ◽  
Multiblock Copolymers ◽  
First Order ◽  
Morphological Studies ◽  
Transmission Electron ◽  
First Order Phase Transition ◽  
Covalently Bonded ◽  
Total Molecular Weight ◽  
First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

Exact First Order Finite Element Modeling for Eddy Current NDE

1991 ◽  
Vol 3 (1) ◽  
pp. 235-253 ◽  
Author(s):  
L. D. Philipp ◽  
Q. H. Nguyen ◽  
D. D. Derkacht ◽  
D. J. Lynch ◽  
A. Mahmood
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Eddy Current ◽  
Element Modeling ◽  
First Order ◽  
Eddy Current Nde

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

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