The One-Variable Fragment of Corsi Logic

Caicedo, Xavier; Metcalfe, George; Rodríguez, Ricardo Óscar; Tuyt, Olim

doi:10.1007/978-3-662-59533-6_5

Cited by 4 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result is not new however, since it turns out that W, π validates (T ) and (T ♦ ) iff π is such that π(w) = 1 for every w ∈ W . In other words, Π 5 G is in fact the class of universal models, the simplified semantics for S5(G), a result that is well-known in the literature [8].…”

Section: By Hypothesis We Know ν(mentioning

confidence: 77%

Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions

et al. 2022

View full text Add to dashboard Cite

In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic $$\mathbf{G}$$ G . More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ , where W is a non-empty set of worlds and $$\pi : W \mathop {\rightarrow }[0,1]$$ π : W → [ 0 , 1 ] is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ where $$\pi $$ π satisfies the normalisation condition $$\sup _{w \in W} \pi (w) = 1$$ sup w ∈ W π ( w ) = 1 .

show abstract

Section: By Hypothesis We Know ν(mentioning

confidence: 77%

Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions

et al. 2022

View full text Add to dashboard Cite

show abstract

“…However this result is not new, since it turns out that (W, π) validates (T ✷ ) and (T ✸ ) iff π is such that π(w) = 1 for every w ∈ W . In other words, Π 5 G is in fact the class of universal models, the simplified semantics for S5(G), a result that is well-known in the literature [7].…”

Section: By Hypothesis We Knowmentioning

confidence: 77%

Simplified Kripke semantics for K45-like Godel modal logics and its axiomatic extensions

Rodríguez¹,

Tuyt²,

Godo³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

One Variable Relevant Logics are S5ish

Ferenz

2024

J Philos Logic

View full text Add to dashboard Cite

Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain S5ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic L, a formula $$\mathcal {A}$$ A of the one-variable fragment is a theorem of LQ (QL) iff its translation is a theorem of L5 (L.5). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for quantified L are transformed into ternary (plus two binary) relational semantics for S5-like extensions of L (for a general presentation, see Seki [26, 27]). In the other direction, a valuation is given for the full first-order relevant logic based on L into a model for a suitable S5 extension of L. I also discuss this work’s relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which RQ is incomplete [11].

show abstract

The One-Variable Fragment of Corsi Logic

Cited by 4 publications

References 14 publications

Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions

Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions

Simplified Kripke semantics for K45-like Godel modal logics and its axiomatic extensions

One Variable Relevant Logics are S5ish

Contact Info

Product

Resources

About