Normal monomodal logics can simulate all others

Kracht, Marcus; Wolter, Frank

doi:10.2307/2586754

Cited by 52 publications

(47 citation statements)

References 24 publications

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“…ψ" that can be derived from our prenex law. 6 For a change, we give a semantic proof for these claims. Let M be a model and s an assignment of objects to variables.…”

Section: Algebraic Content and Proof Analysismentioning

confidence: 98%

On A New Semantics for First-Order Predicate Logic

2017

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Introduction Aldo Antonelli's untimely death is a sad loss to our profession. We have been asked by the editors of the Journal of Philosophical Logic to write a short comment on his most recent work, published in this issue, based in part on a referee report by one of us, that, unfortunately, did not reach Aldo in time.Here is what appeals to us in the innovative work in [4,5]. There is a long history of attempts to reanalyze the semantics of first-order predicate logic, the most basic system in our field. What many of these attempts have in common is a search for specific parameters in the 'standard semantics' given by Tarski that might be naturally modified or generalized. A further motive has been the issue whether the famous 'undecidability of predicate logic' is truly an intrinsic inescapable property of this system, or a side effect of decisions concerning its semantic design that could

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“…ψ" that can be derived from our prenex law. 6 For a change, we give a semantic proof for these claims. Let M be a model and s an assignment of objects to variables.…”

Section: Algebraic Content and Proof Analysismentioning

confidence: 98%

On A New Semantics for First-Order Predicate Logic

2017

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“…Completeness can be proved by means of canonical models. We show that CoPC interprets MPC by means of a sound translation, and complete the chain of translations from CoPC to CPC by a translation of IPC into MPC appearing in the correspondence between Johansson and Heyting in 1935. For future work, the first step is allowing the negation function N to be partial (compare to neighborhood models of modal logic Došen 1989;Kracht and Wolter 1999). This produces more natural and general canonical models.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Subminimal negation

2016

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Minimal logic, i.e., intuitionistic logic without the ex falso principle, is investigated in its original form with a negation symbol instead of a symbol denoting the contradiction. A Kripke semantics is developed for minimal logic and its sublogics with a still weaker negation by introducing a function on the upward closed sets of the models. The basic logic is a logic in which the negation has no properties but the one of being a unary operator. A number of extensions is studied of which the most important ones are contraposition logic and negative ex falso, a weak form of the ex falso principle. Completeness is proved, and the created semantics is further studied. The negative translation of classical logic into intuitionistic logic is made part of a chain of translations by introducing translations from minimal logic into contraposition logic and intuitionistic logic into minimal logic, the latter having been discovered in the correspondence between Johansson and Heyting. Finally, as a bridge to the work of Franco Montagna a start is made of a study of linear models of these logics.Dedicated to the memory of Franco Montagna.

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“…First, the semantic study of non-normal classical systems is either impossible or indirect and unnecessarily complicated (some monotonic non-normal systems can be simulated in terms of polymodal normal logics -see [37]). This is particularly important given the fact that many interesting modal logics of interest in computer science and philosophy are non-normal.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

First-Order Classical Modal Logic

Arló-Costa

Pacuit

2006

Stud Logica

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Abstract.The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics.We conclude by introducing general first order neighborhood frames and we offer a general completeness result in terms of them which circumvents some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of neighborhood frames). We argue that the semantical program that thus arises surpasses both in expressivity and adequacy the standard Kripkean approach, even when it comes to the study of first order normal systems.

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Normal monomodal logics can simulate all others

Cited by 52 publications

References 24 publications

On A New Semantics for First-Order Predicate Logic

On A New Semantics for First-Order Predicate Logic

Subminimal negation

First-Order Classical Modal Logic

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