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Infinitary Logics and 01 Laws
 Information and Computation
, 1992
"... We investigate the in nitary logic L 1! , in which sentences may have arbitrary disjunctions and conjunctions, but they involve only a nite number of distinct variables. We show that various xpoint logics can be viewed as fragments of L 1! , and we describe a gametheoretic characterizat ..."
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Cited by 47 (5 self)
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We investigate the in nitary logic L 1! , in which sentences may have arbitrary disjunctions and conjunctions, but they involve only a nite number of distinct variables. We show that various xpoint logics can be viewed as fragments of L 1! , and we describe a game
Coalgebraic Logic
 Annals of Pure and Applied Logic
, 1999
"... We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula. The ..."
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Cited by 110 (0 self)
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. The point of our generalization is to understand this on a deeper level. We do this by studying a frangment of infinitary modal logic which contains the characterizing formulas and is closed under infinitary conjunction and an operation called 4. This fragment generalizes to a wide range of coalgebraic
Infinitary Modal Logic and Generalized Kripke Semantics
"... This paper deals with the infinitary modal propositional logic K!1, featuring countable disjunctions and conjunctions. It is known that the natural infinitary extension LK⇤!1 (here presented as a Taitstyle calculus, TK!1) of the standard sequent calculus LK⇤p for the propositional modal logic K is ..."
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This paper deals with the infinitary modal propositional logic K!1, featuring countable disjunctions and conjunctions. It is known that the natural infinitary extension LK⇤!1 (here presented as a Taitstyle calculus, TK!1) of the standard sequent calculus LK⇤p for the propositional modal logic K
S.: NonCommutative Infinitary Peano Arithmetic
 In: Proceedings of CSL 2011
, 2011
"... Does there exist any sequent calculus such that it is a subclassical logic and it becomes classical logic when the exchange rules are added? The first contribution of this paper is answering this question for infinitary Peano arithmetic. This paper defines infinitary Peano arithmetic with noncommut ..."
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Cited by 2 (1 self)
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and specifically the commutativity for conjunction and disjunction is derivable. This paper shows that the provability in noncommutative infinitary Peano arithmetic is equivalent to Heyting arithmetic with the recursive omega rule and the law of excluded middle for Sigma01 formulas. Thus, non
An Infinitary Graded Modal Logic (Graded Modalities VI)l)
"... Abstract. We prove a completeness theorem for K:l, the infinitary extension of the graded version K O of the minimal normal logic K, allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities and ..."
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Abstract. We prove a completeness theorem for K:l, the infinitary extension of the graded version K O of the minimal normal logic K, allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities
A Logical Characterization of Bisimulation for Labeled Markov Processes
"... This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [5]. ffl Bisimulation can be characterized by a very weakmodal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be charac ..."
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Cited by 41 (11 self)
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be characterized by several inequivalent logics; we report five in this paper and there are surely many more. ffl We do not need any finite branching assumption yetthere is no need of infinitary conjunction. ffl We give an algorithm for deciding bisimilarity of finite state systems which constructs a formula
Robert Goldblatt Grishin Algebras and Cover Systems for Classical Bilinear Logic
"... Abstract. Grishin algebras are a generalisation of Boolean algebras that provide algebraic models for classical bilinear logic with two mutually cancelling negation connectives. We show how to build complete Grishin algebras as algebras of certain subsets (“propositions”) of cover systems that use a ..."
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. This representation is then used to give a cover system semantics for a version of classical bilinear logic that has firstorder quantifiers and infinitary conjunctions and disjunctions.
Propositional fuzzy logics based on Frank tnorms: A comparison
, 1999
"... Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from different basic logical connectives, they both use interpretations based on Frank tnorms. Different interpretations of the implication lead to different axiomatizati ..."
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Cited by 1 (1 self)
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axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages of the two approaches. We deal also with logics containing infinitary conjunctions, and we show that they are semantically "stronger" than all the other logics studied in this paper
Finitary Sketches
, 1997
"... Finitary sketches, i.e., sketches with finitelimit and finitecolimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finitelimit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary firstorder ..."
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Cited by 7 (0 self)
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Finitary sketches, i.e., sketches with finitelimit and finitecolimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finitelimit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first
Relatively recursive expansions*
"... Abstract. In this paper, we consider the following basic question. Let A be an Lstructure and let ψ be an infinitary sentence in the language L ∪ {R}, where R is a new relation symbol. When is it the case that for every B ∼ = A, there is a relation R such that (B, R)�ψ and R ≤T D(B)? We succeed in ..."
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in giving necessary and sufficient conditions in the case where ψ is a “recursive ” infinitary Π2 sentence. (A recursive infinitary formula is an infinitary formula with recursive disjunctions and conjunctions.) We consider also some variants of the basic question, in which R is r.e., ∆ 0 α, or Σα instead
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