In S. Lambropoulou, D. Theodorou, P. Stefaneas & L. H. Kauffman (Eds), Algebraic Modeling of Topological and Computational Structures and Applications, Springer, PROMS series, 2017
This paper constitutes a first attempt at constructing semantic theories
over institutions and e... more This paper constitutes a first attempt at constructing semantic theories
over institutions and examining the logical relations holding between different such
theories. Our results show that this approach can be very useful for theoretical computer
science (and may also contribute to the current philosophical debate regarding
the semantic and the syntactic presentation of scientific theories). First we provide
a definition of semantic theories in the institution theory framework - in terms of a
set of models satisfying a given set of sentences - using the language-independent
satisfaction relation characterizing institutions (Definition 3). Then we give a proof
of the logical equivalence holding between the syntactic and the semantic presentation
of a theory, based on the Galois connection holding between sentences and
models (Theorem 1).We also show how to integrate and combine semantic theories
using colimits (Theorem 2). Finally we establish when the output of a model-based
software verification method applied to a semantic theory over an institution also
holds for a semantic theory defined over a different institution (Theorem 3).
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Papers by Nicola Angius
over institutions and examining the logical relations holding between different such
theories. Our results show that this approach can be very useful for theoretical computer
science (and may also contribute to the current philosophical debate regarding
the semantic and the syntactic presentation of scientific theories). First we provide
a definition of semantic theories in the institution theory framework - in terms of a
set of models satisfying a given set of sentences - using the language-independent
satisfaction relation characterizing institutions (Definition 3). Then we give a proof
of the logical equivalence holding between the syntactic and the semantic presentation
of a theory, based on the Galois connection holding between sentences and
models (Theorem 1).We also show how to integrate and combine semantic theories
using colimits (Theorem 2). Finally we establish when the output of a model-based
software verification method applied to a semantic theory over an institution also
holds for a semantic theory defined over a different institution (Theorem 3).
The philosophy of computer science is concerned with those philosophical issues that arise from within the academic discipline of computer science. It is intended to be the philosophical endeavor that stands to computer science as philosophy of mathematics does to mathematics and philosophy of technology does to technology. Indeed, the abstract nature of computer science, coupled with its technological ambitions, ensures that many of the conceptual questions that arise in the philosophies of mathematics and technology have computational analogues. In addition, the subject will draw in variants of some of the central questions in the philosophies of mind, language and science. We shall concentrate on a tightly related group of topics which form the spine of the subject. These include specification, implementation, semantics, programs, programming, correctness, abstraction and computation."
over institutions and examining the logical relations holding between different such
theories. Our results show that this approach can be very useful for theoretical computer
science (and may also contribute to the current philosophical debate regarding
the semantic and the syntactic presentation of scientific theories). First we provide
a definition of semantic theories in the institution theory framework - in terms of a
set of models satisfying a given set of sentences - using the language-independent
satisfaction relation characterizing institutions (Definition 3). Then we give a proof
of the logical equivalence holding between the syntactic and the semantic presentation
of a theory, based on the Galois connection holding between sentences and
models (Theorem 1).We also show how to integrate and combine semantic theories
using colimits (Theorem 2). Finally we establish when the output of a model-based
software verification method applied to a semantic theory over an institution also
holds for a semantic theory defined over a different institution (Theorem 3).
The philosophy of computer science is concerned with those philosophical issues that arise from within the academic discipline of computer science. It is intended to be the philosophical endeavor that stands to computer science as philosophy of mathematics does to mathematics and philosophy of technology does to technology. Indeed, the abstract nature of computer science, coupled with its technological ambitions, ensures that many of the conceptual questions that arise in the philosophies of mathematics and technology have computational analogues. In addition, the subject will draw in variants of some of the central questions in the philosophies of mind, language and science. We shall concentrate on a tightly related group of topics which form the spine of the subject. These include specification, implementation, semantics, programs, programming, correctness, abstraction and computation."