scholarly journals A Note on Algebraic Semantics for $\mathsf{S5}$ with Propositional Quantifiers

2019 ◽  
Vol 60 (2) ◽  
pp. 311-332
Author(s):  
Wesley H. Holliday
Keyword(s):  
Algebraic Semantics ◽  
Propositional Quantifiers

Quantifying over propositions in relevance logic: nonaxiomatisability of primary interpretations of ∀p and ∃p

1993 ◽  
Vol 58 (1) ◽  
pp. 334-349 ◽  
Author(s):  
Philip Kremer
Keyword(s):  
Relevance Logic ◽  
Algebraic Semantics ◽  
Algebraic Structures ◽  
Propositional Quantifiers

A typical approach to semantics for relevance (and other) logics: specify a class of algebraic structures and take a model to be one of these structures, α, together with some function or relation which associates with every formula A a subset of α. (This is the approach of, among others, Urquhart, Routley and Meyer and Fine.) In some cases there are restrictions on the class of subsets of α with which a formula can be associated: for example, in the semantics of Routley and Meyer [1973], a formula can only be associated with subsets which are closed upwards. It is natural to take a proposition of α to be such a subset of α, and, further, to take the propositional quantifiers to range over these propositions. (Routley and Meyer [1973] explicitly consider this interpretation.) Given such an algebraic semantics, we call (following Routley and Meyer [1973], who follow Henkin [1950]) the above-described interpretation of the quantifiers the primary interpretation associated with the semantics.

Parts of a Whole

2017 ◽  
Author(s):  
Lucas Champollion
Keyword(s):  
Algebraic Semantics ◽  
Reference Measurement ◽  
Single Constraint ◽  
Starting Point ◽  
Accessible Format ◽  
The Way

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.

scholarly journals Filters and congruences in sectionally pseudocomplemented lattices and posets

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.

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

2010 ◽  
Vol 180 (8) ◽  
pp. 1354-1372 ◽  
Author(s):  
Carles Noguera ◽  
Francesc Esteva ◽  
Lluís Godo
Keyword(s):  
Algebraic Semantics ◽  
Fuzzy Logics

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

SIMULATION ◽  
2008 ◽  
Vol 84 (7) ◽  
pp. 339-358 ◽  
Author(s):  
Pieter J.L. Cuijpers ◽  
Jan F. Broenink ◽  
Pieter J. Mosterman
Keyword(s):  
Algebraic Semantics ◽  
Bond Graphs ◽  
Hybrid Processes ◽  
Process Algebraic

scholarly journals Higher-Order Illative Combinatory Logic

2013 ◽  
Vol 78 (3) ◽  
pp. 837-872 ◽  
Author(s):  
Łukasz Czajka
Keyword(s):  
Strong Consistency ◽  
Predicate Logic ◽  
Higher Order ◽  
Second Order ◽  
Model Construction ◽  
Partial Answer ◽  
Combinatory Logic ◽  
First Order ◽  
Propositional Quantifiers

AbstractWe show a model construction for a system of higher-order illative combinatory logic thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system of Barendregt, Bunder and Dekkers, which gives a partial answer to a question posed by these authors.

An abstract algebraic logic approach to tetravalent modal logics

2000 ◽  
Vol 65 (2) ◽  
pp. 481-518 ◽  
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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