524 research outputs found
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
G\"odel's Notre Dame Course
This is a companion to a paper by the authors entitled "G\"odel's natural
deduction", which presented and made comments about the natural deduction
system in G\"odel's unpublished notes for the elementary logic course he gave
at the University of Notre Dame in 1939. In that earlier paper, which was
itself a companion to a paper that examined the links between some
philosophical views ascribed to G\"odel and general proof theory, one can find
a brief summary of G\"odel's notes for the Notre Dame course. In order to put
the earlier paper in proper perspective, a more complete summary of these
interesting notes, with comments concerning them, is given here.Comment: 18 pages. minor additions, arXiv admin note: text overlap with
arXiv:1604.0307
Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate
Decidability of predicate logics with team semantics
We study the complexity of predicate logics based on team semantics. We show
that the satisfiability problems of two-variable independence logic and
inclusion logic are both NEXPTIME-complete. Furthermore, we show that the
validity problem of two-variable dependence logic is undecidable, thereby
solving an open problem from the team semantics literature. We also briefly
analyse the complexity of the Bernays-Sch\"onfinkel-Ramsey prefix classes of
dependence logic.Comment: Extended version of a MFCS 2016 article. Changes on the earlier arXiv
version: title changed, added the result on validity of two-variable
dependence logic, restructurin
A Simple Logic of Functional Dependence
This paper presents a simple decidable logic of functional dependence LFD,
based on an extension of classical propositional logic with dependence atoms
plus dependence quantifiers treated as modalities, within the setting of
generalized assignment semantics for first order logic. The expressive
strength, complete proof calculus and meta-properties of LFD are explored.
Various language extensions are presented as well, up to undecidable
modal-style logics for independence and dynamic logics of changing dependence
models. Finally, more concrete settings for dependence are discussed:
continuous dependence in topological models, linear dependence in vector
spaces, and temporal dependence in dynamical systems and games.Comment: 56 pages. Journal of Philosophical Logic (2021
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
A Logic for True Concurrency
We propose a logic for true concurrency whose formulae predicate about events
in computations and their causal dependencies. The induced logical equivalence
is hereditary history preserving bisimilarity, and fragments of the logic can
be identified which correspond to other true concurrent behavioural
equivalences in the literature: step, pomset and history preserving
bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving)
bisimilarity, is also recovered as a fragment. We also propose an extension of
the logic with fixpoint operators, thus allowing to describe causal and
concurrency properties of infinite computations. We believe that this work
contributes to a rational presentation of the true concurrent spectrum and to a
deeper understanding of the relations between the involved behavioural
equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201
Insights into Modal Slash Logic and Modal Decidability
The present paper has a two-fold task. On the one hand, it aims to provide an overview on Independence friendly modal logic as defined in (Tulenheimo, 2003; Tulenheimo, 2004) and studied in a number of subsequent publications. For systematic reasons to be explained, the logic is here referred to as modal slash logic (MsL). On the other hand, we take a close look at a syntactic fragment of MsL, to be termed MsL0, first formulated in (Tulenheimo and Sevenster, 2006). We push the study of this logic deeper at several points: a model-theoretic criterion is presented which serves to tell when a formula of MsL0 is not truth-equivalent to any formula of basic modal logic (ML); the game-theoretic property of ‘bounded quasi-positionality' of MsL0 is studied in detail; an alternative syntax for MsL0 is discerned and the logic obtained is shown to enjoy the property of quasi-locality (generalizing the notion of locality familiar from ML); and we formulate an asymmetric bisimulation
concept and use it to prove that MsL0 is not closed under complementation. Drawing from insights provided by the study of MsL0, we conclude by general observations about claims made on the ‘reasons' why various modal logics are computationally well-behaved
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