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A complete axiomatization of infinitary first-order intuitionistic logic over ℒ_κ ^+, κ
[article]
2020
arXiv
pre-print
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When κ is a regular cardinal such that κ ^<κ =κ , we deduce, by an easy modification of the proof, a complete axiomatization of intuitionistic first-order logic over ℒ_κ ^+, κ , κ , the language with disjunctions ...
Given a weakly compact cardinal κ , we give an axiomatization of intuitionistic first-order logic over ℒ_κ ^+, κ and prove it is sound and complete with respect to Kripke models. ...
Introduction Completeness theorems for infinitary intuitionistic logics begun to be studied by the end of the 1970's. ...
arXiv:1806.06714v5
fatcat:tzknlj5p4jgaxnqb7nnrycpily
A completeness proof for an infinitary tense-logic
2008
Theoria
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H. von Wright's tense-logic [4] , Krister Segerberg studies certain infinitary extensions of the original tense-logic created by von Wright. ...
For one of these extensions the completeness problem turned out to be harder than was expected at first sight. 1 This paper is devoted to a proof of a completeness theorem for the extension in question ...
H. von Wright's tense-logic [4] , Krister Segerberg studies certain infinitary extensions of the original tense-logic created by von Wright. ...
doi:10.1111/j.1755-2567.1977.tb00778.x
fatcat:x3cc74jbvbfy5ggpb3afqe4d2e
The Ackermann Award 2018
2018
Annual Conference for Computer Science Logic
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The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. It is presented during the annual conference of the EACSL (CSL'xx). ...
Another large part studies the infinitary proof theory of a fixpoint extension of multiplicative additive linear logic, a challenging topic due to the non-well-founded nature of infinitary proofs. ...
By identifying new connections between infinitary proofs and automata theory (e.g., non-determinization of alternating parity automata), she has managed to obtain a new constructive completeness argument ...
doi:10.4230/lipics.csl.2018.1
dblp:conf/csl/KozenS18
fatcat:enjy7e5ltvbarlumyxu5tzq2zy
Infinitary equilibrium logic and strongly equivalent logic programs
2017
Artificial Intelligence
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This is useful because of the relationship between infinitary formulas and logic programs with local variables. ...
We extend this line of work to formulas with infinitely long conjunctions and disjunctions, show that the infinitary logic of here-and-there characterizes strong equivalence of infinitary formulas, and ...
Stable Models and Equilibrium Logic in the Infinitary Setting
Review: Infinitary Formulas Let Σ be a propositional signature, that is, a set of propositional atoms. ...
doi:10.1016/j.artint.2017.02.002
fatcat:wbv5o7de5nfelin4fut7zrxdqm
Infinitary Equilibrium Logic and Strong Equivalence
[chapter]
2015
Lecture Notes in Computer Science
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We extend equilibrium logic to formulas with infinitely long conjunctions and disjunctions, define and axiomatize an infinitary counterpart to the logic of here-and-there, and show that the theorem on ...
strong equivalence holds in the infinitary case as well. ...
The proof of completeness given in the next section is analogous to the proof of completeness for classical propositional logic from [7] . ...
doi:10.1007/978-3-319-23264-5_33
fatcat:ireikpz6pzexrptt7rblwslpbu
An extension of Jónsson-Tarski representation and model existence in predicate non-normal modal logics
[article]
2023
arXiv
pre-print
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Then, we show that every predicate modal logic, whether it is normal or non-normal, has a model defined on a neighborhood frame with constant domains, and give completeness theorem for some predicate modal ...
We also show the same results for infinitary modal logics. ...
As a corollary, we give completeness theorem for some infinitary modal logics, including the least infinitary extension K ω 1 of K. ...
arXiv:2103.16857v3
fatcat:xnk3q7esqrdivntwhoc7bimrim
Hybrid Logics with Infinitary Proof Systems
2006
Journal of Logic and Computation
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We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. ...
Moreover a finitary proof system cannot be strongly complete for such logics, since they are not compact. Therefore we focus on infinitary proof systems. ...
Our proof is inspired by the completeness proofs for the infinitary logic L ω 1 ω in [9] , the strong completeness proof for infinitary modal logics in [7] , and the completeness proof for finitary hybrid ...
doi:10.1093/logcom/exi086
fatcat:zhf34jp4ezeo5icrd7qp6fudoi
Supervenience and Infinitary Logic
2001
Noûs
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The discussion of supervenience is replete with the use of infinitary logical operations. ...
Some philosophers have been troubled simply by the infinity of such a disjunction. ...
In section (5), I show that considering infinitary logic leads to a puzzle about the complete physical state of the universe. ...
doi:10.1111/0029-4624.00304
fatcat:wchgj7cjjzedfj2jeugzsssfxq
Sequent systems for PLTL
2013
Lietuvos matematikos rinkinys
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calculi with looping axioms and with invariant-like rule based on completeness of the calculus with the infinitary $\omega$-type rule. ...
We consider three sequent calculi for propositional linear temporal logic (PLTL) which allow us to formalize the properties of operator "always". ...
The infinitary calculus G ω T is defined by the following postulates: 2. Traditional logical rules; 3. Temporal rules: Γ → ∆ Π , Γ → Θ , ∆ ( ), A, A, Γ → ∆ A, Γ → ∆ ( →), Γ → ∆, A; Γ → ∆, A; . . . ...
doi:10.15388/lmr.a.2013.03
fatcat:kqxacrpfyvbadmuavwmjw5t5ei
Classifying toposes for non-geometric theories
[article]
2023
arXiv
pre-print
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Along the way we obtain completeness results of infinitary sub-first-order logic and infinitary classical logic with respect to (Boolean) toposes. ...
We study classifying toposes for different infinitary logics: first-order, sub-first-order (i.e. geometric logic plus implication) and classical. ...
A similar statement is true for infinitary first-order logic and geometric logic (which are included in Theorem 5.7 for completeness' sake), but those are not new in this paper. • Theorem 5.11 (classical ...
arXiv:2312.11528v1
fatcat:gaign2uf55dmrip4u6zbfreuse
Infinitary logic and basically disconnected compact Hausdorff spaces
2018
Journal of Logic and Computation
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2017 pre-print arXiv:1709.08397v1 fatcat:bdm26w62c5cihnkhf2qelp5rxmOther Versions
We extend Ł ukasiewicz logic obtaining the infinitary logic IRŁ whose models are algebras C(X,[0,1]), where X is a basically disconnected compact Hausdorff space. ...
Finally, our system enjoys standard completeness with respect to the real interval [0,1]. ...
definition of a norm-complete Riesz MV-algebra. of the infinitary classical logic. ...
doi:10.1093/logcom/exy011
fatcat:5ynrkxkxdbb2nknctgu2lem23i
The monotone class theorem in infinitary logic
1977
Proceedings of the American Mathematical Society
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Here we discuss more traditional infinitary logics. ...
A monotone formula in the infinitary logic L is a formula which is built up from finite formulas using only quantifiers and monotone countable conjunctions and disjunctions. ...
For background material on infinitary logic and admissible sets see Barwise [1] . ...
doi:10.1090/s0002-9939-1977-0441686-2
fatcat:trxtkgnfuzehvk7wnc75iimxgy
Page 7023 of Mathematical Reviews Vol. , Issue 2002J
[page]
2002
Mathematical Reviews
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“In this paper, I investigate the interaction between superve- nience and infinitary logic. Supervenience has long been a point of contact between logic and metaphysics. ...
Infinitary logical operations have been studied in depth by the highly developed field of infinitary logic, and many of their prop- erties are well understood. ...
Expressive power of infinitary [0, 1]-valued logics
[article]
2017
arXiv
pre-print
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We then prove that a continuous function on a complete separable metric structure is automorphism invariant if and only if it is definable in the more expressive logic. ...
We give an example showing that one of these infinitary logics is strictly more expressive than the other two, but also show that all three have the same elementary equivalence relation for complete separable ...
We thank both supervisors for their suggestions and insights, both on the work specifically represented here, and on infinitary logic ...
arXiv:1512.00879v2
fatcat:3ezkudhbcjbk5j6bi56g5dchjq
"Mathematics is the Logic of the Infinite": Zermelo's Project of Infinitary Logic
2021
Studies in Logic, Grammar and Rhetoric
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In this paper I discuss Ernst Zermelo's ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. ...
The presentation of Zermelo's ideas is accompanied with some remarks concerning the development of infinitary logic. ...
Infinitary logics with infinite quantifier prefixes are close to second-order
logic and hence they do not satisfy the completeness theorem. ...
doi:10.2478/slgr-2021-0042
fatcat:nnowhogl3bhklm234xa7dion7u
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