Semantic Properties of Computations Defined by Elementary Inference Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908620126420992 |
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| author | Lucas, Salvador |
| author_facet | Lucas, Salvador |
| contents | We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n), where predicate P represents the considered set/relation/computation. A first-order theory Th(I), actually a set of definite Horn clauses, is given to I. Properties of objects defined by I are expressed as first-order sentences F, which are proved true or false by *satisfaction* M |= F of F in a *canonical* model M of Th(I). For this reason, we call F a *semantic property* of I. Since canonical models are, in general, incomputable, we show how to (dis)prove semantic properties by satisfiability in an *arbitrary* model A of Th(I). We apply these ideas to the analysis of properties of programming languages and systems whose computations can be described by means of an elementary inference system. In particular, rewriting-based systems.
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| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semantic Properties of Computations Defined by Elementary Inference Systems Lucas, Salvador Logic in Computer Science Programming Languages Symbolic Computation We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n), where predicate P represents the considered set/relation/computation. A first-order theory Th(I), actually a set of definite Horn clauses, is given to I. Properties of objects defined by I are expressed as first-order sentences F, which are proved true or false by *satisfaction* M |= F of F in a *canonical* model M of Th(I). For this reason, we call F a *semantic property* of I. Since canonical models are, in general, incomputable, we show how to (dis)prove semantic properties by satisfiability in an *arbitrary* model A of Th(I). We apply these ideas to the analysis of properties of programming languages and systems whose computations can be described by means of an elementary inference system. In particular, rewriting-based systems. |
| title | Semantic Properties of Computations Defined by Elementary Inference Systems |
| topic | Logic in Computer Science Programming Languages Symbolic Computation |
| url | https://arxiv.org/abs/2510.26429 |