Weak islands and an algebraic semantics for scope taking

Why can I tell you that I ran for five minutes but not that I *ran all the way to the store for five minutes? Why can you say that there are five pounds of books in this package if it contains several books, but not *five pounds of book if it contains only one? What keeps you from using *sixty degrees of water to tell me the temperature of the water in your pool when you can use sixty inches of water to tell me its height? And what goes wrong when I complain that *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. This work provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above. This provides a starting point from which various linguistic applications of mereology are developed and explored. The main foundational issues, relevant data, and choice points are introduced in an accessible format.

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Filters and congruences in sectionally pseudocomplemented lattices and posets

Soft Computing ◽

10.1007/s00500-021-05900-4 ◽

2021 ◽

Author(s):

Ivan Chajda ◽

Helmut Länger

Keyword(s):

Algebraic Semantics ◽

Basic Properties ◽

Algebraic Constructions ◽

Pseudocomplemented Lattices ◽

Intuitionistic Logics

AbstractTogether with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that—similar to relatively pseudocomplemented lattices—these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters in both sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e., ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.

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Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics

Information Sciences ◽

10.1016/j.ins.2009.12.011 ◽

2010 ◽

Vol 180 (8) ◽

pp. 1354-1372 ◽

Cited By ~ 14

Author(s):

Carles Noguera ◽

Francesc Esteva ◽

Lluís Godo

Keyword(s):

Algebraic Semantics ◽

Fuzzy Logics

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Constitutive Hybrid Processes: a Process-Algebraic Semantics for Hybrid Bond Graphs

SIMULATION ◽

10.1177/0037549708097215 ◽

2008 ◽

Vol 84 (7) ◽

pp. 339-358 ◽

Cited By ~ 5

Author(s):

Pieter J.L. Cuijpers ◽

Jan F. Broenink ◽

Pieter J. Mosterman

Keyword(s):

Algebraic Semantics ◽

Bond Graphs ◽

Hybrid Processes ◽

Process Algebraic

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Linking Algebraic Semantics and Operational Semantics for Web Services Using Maude

2013 18th International Conference on Engineering of Complex Computer Systems ◽

10.1109/iceccs.2013.46 ◽

2013 ◽

Cited By ~ 1

Author(s):

Peng Liu ◽

Huibiao Zhu ◽

Shengchao Qin ◽

Phillip J. Brooke ◽

Xi Wu

Keyword(s):

Web Services ◽

Operational Semantics ◽

Algebraic Semantics

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An abstract algebraic logic approach to tetravalent modal logics

Journal of Symbolic Logic ◽

10.2307/2586552 ◽

2000 ◽

Vol 65 (2) ◽

pp. 481-518 ◽

Cited By ~ 15

Author(s):

Josep Maria Font ◽

Miquel Rius

Keyword(s):

Algebraic Logic ◽

Modal Logics ◽

The Other ◽

Abstract Algebraic Logic ◽

Algebraic Semantics ◽

Modal Algebras ◽

Logic Approach ◽

Abstract Logics ◽

Joint Study

AbstractThis paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their “A General Algebraic Semantics for Sentential Logics”. The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo. Landini and Ziliani, at the suggestion of the late Antonio Monteiro.

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