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1

Palsberg, Jens, ed. Semantics and Algebraic Specification. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04164-8.

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2

M, Nivat, and Reynolds John C. 1935-, eds. Algebraic methods in semantics. Cambridge [Cambridgeshire]: Cambridge University Press, 1985.

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3

Manes, Ernest G., and Michael A. Arbib. Algebraic Approaches to Program Semantics. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4962-7.

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4

Grant, Malcolm, ed. Algebraic semantics of imperative programs. Cambridge, Mass: MIT Press, 1996.

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5

Manes, Ernest G. Algebraic Approaches to Program Semantics. New York, NY: Springer New York, 1986.

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6

A, Arbib Michael, ed. Algebraic approaches to program semantics. New York: Springer-Verlag, 1986.

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7

Mäder, Roman E. Graph algebras, algebraic and denotational semantics. Zürich: ETH, 1986.

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8

Font, Josep Maria, and Ramon Jansana. A General Algebraic Semantics for Sentenial Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-21591-3.

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9

Ramón, Jansana, ed. A general algebraic semantics for sentential logics. Berlin: Springer-Verlag, 1996.

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10

Milner, Robin. Operational and algebraic semantics of concurrent processes. Edinburgh: University of Edinburgh, Laboratoryfor Foundations of Computer Sciences, 1988.

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11

Linde-Göers, Hans-Günther. Compositional partial order semantics of Petri boxes. Aachen: Verlag Shaker, 1994.

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12

Ehrig, Hartmut. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985.

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13

1934-, Burstall R. M., Goguen Joseph, Tarlecki Andrzej, and University of Edinburgh. Laboratory for Foundations of Computer Science., eds. Some fundamental algebraic tools for the semantics of computation. Edinburgh: University of Edinburgh Laboratory for Foundations of Computer Science, 1988.

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14

Hennessy, Matthew. Algebraic theory of processes. Cambridge, Mass: MIT Press, 1988.

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15

Hennessy, Matthew. Algebraic theory of processes. Cambridge, MA: MIT Press, 1988.

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16

Burstall, R. M. Some fundamental algebraic tools for the semantics of computation part 3: Indesced Categories. Edinburgh: University of Edinburgh, Laboratory for Foundations in Computer Science, 1989.

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17

Czelakowski, Janusz. Protoalgebraic Logics. Dordrecht: Springer Netherlands, 2001.

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18

Reichel, Horst. Initial computability, algebraic specifications, and partial algebras. Berlin: Akademie-Verlag, 1987.

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19

Girish, Bhat, Cleaveland Rance, and Langley Research Center, eds. A practical approach to implementing real-time semantics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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20

Girish, Bhat, Cleaveland Rance, and Langley Research Center, eds. A practical approach to implementing real-time semantics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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21

der, Beeck Michael von, Cleaveland Rance, and Langley Research Center, eds. Statecharts via process algebra. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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22

Makkai, Mihály. Models, logics, and higher-dimensional categories: A tribute to the work of Mihaly Makkai. Providence, R.I: American Mathematical Society, 2011.

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23

Aceto, Luca. Action refinement in process algebras. Cambridge: Cambridge University Press, 1992.

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24

Ching-man, Au Yeung, and Leung Ho-Fung, eds. Fuzzy computational ontologies in contexts: Formal models of knowledge representation with membership degree and typicality of objects, and their applications. Beijing: Higher Education Press, 2012.

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25

Arbib, Michael A., and Ernest G. Manes. Algebraic Approaches to Program Semantics. Springer, 2014.

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26

Manes, E. G., and M. A. Arbib. Algebraic Approaches To Program Semantics. Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1986.

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27

Algebraic semantics in language and philosophy. Stanford, Calif: CSLI Publications, 1998.

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28

Lapets, Andrei. Algebraic semantics of domain-specific languages. 2006, 2007.

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29

Jansana, Ramon, and Josep Maria Font. General Algebraic Semantics for Sentential Logics. University of Cambridge ESOL Examinations, 2017.

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30

Jansana, Ramon, and Josep Maria Font. General Algebraic Semantics for Sentential Logics. Cambridge University Press, 2017.

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31

Jansana, Ramon, and Josep Maria Font. General Algebraic Semantics for Sentential Logics. Cambridge University Press, 2016.

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32

Jansana, Ramón. A General Algebraic Semantics for Sentenial Logics. 1996.

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33

Bernd, Ehrig Hartmut Mahr. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Springer, 1985.

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34

Ehrig, Hartmut, and Peter Deuflhard. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Springer, 2011.

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35

Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Springer, 2011.

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36

Schlechta, Karl. Coherent Systems. Elsevier Science & Technology Books, 2004.

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37

Fey, Werner. Pragmatics, concepts, syntax, semantics and correctness notions of ACT TWO: An algebraic module specification and interconnection language. 1988.

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38

Semantics And Algebraic Specification Essays Dedicated To Peter D Mosses On The Occasion Of His 60th Birthday. Springer, 2009.

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39

Palsberg, Jens. Semantics and Algebraic Specification: Essays Dedicated to Peter D. Mosses on the Occasion of His 60th Birthday. Springer London, Limited, 2009.

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40

Initial computability, algebraic specifications, and partial algebras. Oxford [England]: Clarendon Press, 1987.

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41

Reichel, Horst. Initial Computability, Algebraic Specifications, and Partial Algebras. de Gruyter GmbH, Walter, 2022.

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42

Initial Computability, Algebraic Specifications, and Partial Algebras. de Gruyter GmbH, Walter, 1988.

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43

Abramsky, S., Dov M. Gabbay, and T. S. E. Maibaum, eds. Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780198537816.001.0001.

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Logic is now widely recognized as one of the foundational disciplines of computing, and its applications reach almost every aspect of the subject, from software engineering and hardware to programming languages and AI. The Handbook of Logic in Computer Science is a multi-volume work covering all the major areas of application of logic to theoretical computer science. The handbook comprises six volumes, each containing five or six chapters giving an in-depth overview of one of the major topics in field. It is the result of many years of cooperative effort by some of the most eminent frontline researchers in the field, and will no doubt be the standard reference work in logic and theoretical computer science for years to come. Volume 5: Algebraic and Logical Structures covers all the fundamental topics of semantics in logic and computation. The extensive chapters are the result of several years of coordinated research, and each have thematic perspective. Together, they offer the reader the latest in research work, and the book will be indispensable
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44

Lassiter, Daniel. Measurement theory and the typology of scales. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198701347.003.0002.

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Most previous work on graded modality has relied on qualitative orderings, rather than degree semantics. This chapter introduces Representational Theory of Measurement (RTM), a framework which makes it possible to translate between qualitative and degree-based scales. I describe a way of using RTM to extend the compositional degree semantics introduced in chapter 1 to qualitative scales. English data are used to motivate the application of the RTM discussion between ordinal, interval, and ratio scales to scalar adjectives, with special attention to the kinds of statements that are semantically interpretable relative to different scale types. I also propose and motivate empirically a distinction between ‘additive’ and ‘intermediate’ scales, which interact differently with the algebraic join operation (realizing sum formation or disjunction, depending on the domain). This distinction is reflected in inferential properties of non-modal adjectives in English, and is also important for the analysis of graded modality in later chapters.
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45

Sapir, Mark V., Victor S. Guba, and Mikhail V. Volkov. Combinatorial Algebra: Syntax and Semantics. Springer London, Limited, 2014.

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46

Guba, Victor S., Mikhail V. Volkov, and Mark V. V. Sapir. Combinatorial Algebra: Syntax and Semantics. Springer, 2016.

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47

Button, Tim, and Sean Walsh. Internal categoricity and the natural numbers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0010.

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The simple conclusion of the preceding chapters is that moderate modelism fails. But this leaves us with a choice between abandoning moderation and abandoning modelism. The aim of this chapter, and the next couple of chapters, is to outline a speculative way to save moderation by abandoning modelism. The idea is to do metamathematics without semantics, by working deductively in a higher-order logic. In this chapter, the focus is on the internal categoricity of arithmetic. After formalising an internal notion of a model of the Peano axioms, we show how to internalise Dedekind’s Categority Theorem. The resulting “intolerance” of Peano arithmetic provides internalists with a way to draw the distinction between algebraic and univocal theories. In the appendices, we discuss how this relates to Parsons’ important work, and establish a certain dependence of the internal categoricity theorem on higher-order logic.
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48

Lambek, Joachim, and H. H. Storrer. Torsion Theories, Additive Semantics, and Rings of Quotients. Springer London, Limited, 2006.

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49

Champollion, Lucas. Parts of a Whole. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198755128.001.0001.

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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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50

Flexibility principles in boolean semantics: The interpretation of coordination, plurality and scope in natural language. Cambridge, Mass: MIT Press, 2001.

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