Search results for "Modal logic"
showing 10 items of 20 documents
Elementary Action Systems
2015
This chapter expounds basic notions. An elementary action system is a triple consisting of the set of states, the transition relation between states, and a family of binary relations defined on the set of states. The elements of this family are called atomic actions. Each pair of states belonging to an atomic action is a possible performance of this action. This purely extensional understanding of atomic actions is close to dynamic logic. Compound actions are defined as sets of finite sequences of atomic actions. Thus compound actions are regarded as languages over the alphabet whose elements are atomic actions. This chapter is concerned with the problem of performability of actions and the…
Unification in first-order transitive modal logic
2019
We introduce unification in first-order transitive modal logics, i.e. logics extending Q–K4, and apply it to solve some problems such as admissibility of rules. Unifiable formulas in some extensions of Q–K4 are characterized and an explicit basis for the passive rules (those with non-unifiable premises) is provided. Both unifiability and passive rules depend on the number of logical constants in the logic; we focus on extensions of Q–K4 with at most four constants ⊤,⊥,□⊥,◊⊤. Projective formulas, defined in a way similar to propositional logic, are used to solve some questions concerning the disjunction and existence properties. A partial characterization of first-order modal logics with pr…
Awareness and Partitional Informational Structures
1997
We begin with an example to motivate the introduction of the concept of unawareness in models of information. There are a subject and two possible states of the world, σ and τ. At σ a certain fact p happens — it is true — and the subject sees it or hears it or anyhow perceives it, so that he knows it is true (in Geanakoplos [5] the subject is Sherlock Holmes’ assistant and fact p is ‘the dog barks’). At state τ fact p does not occur (it is false), and the subject not only does not see it or hear it etc.; but what is more, he does not even think of the possibility that it might: fact p is not present to the subject’s mind. What is an appropriate formal model for this story?
Frames for fusions of modal logics
2018
Let us consider multimodal logics and . We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and , we construct a connected frame which characterises the fusion . The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point . We also describe a similar construction where we assume the existence o…
Finite Model Reasoning in Expressive Fragments of First-Order Logic
2017
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard translation of modal logic to first-order logic. This applies most notably to the guarded fragment, where quantifiers are appropriately relativized by atoms, and the fragment defined by restricting the number of variables to two. The aim of this talk is to review recent work concerning these fragments and their popular extensions. When presenting the material special attention is given to decision procedures for the finite satisfiability problems, as many of t…
Mathematical logic and quantum finite state automata
2009
AbstractThis paper is a review of the connection between formulas of logic and quantum finite-state automata in respect to the language recognition and acceptance probability of quantum finite-state automata. As is well known, logic has had a great impact on classical computation, it is promising to study the relation between quantum finite-state automata and mathematical logic. After a brief introduction to the connection between classical computation and logic, the required background of the logic and quantum finite-state automata is provided and the results of the connection between quantum finite-state automata and logic are presented.
Finitary unification in locally tabular modal logics characterized
2022
We provide necessary and sufficient conditions for finitary unification in locally tabular modal logics, solely in terms of Kripke models. We apply the conditions to establish the unification types of logics determined by simple finite frames. In particular, we show that unification is finitary (or unitary) in the logic determined by the fork (frame F4, see Fig. 6), the rhombus (frame F5), inGL.3m,GrzBd2,S4Bd2and other logics; whereas it is nullary in the logic of F6, and of the pentagon FN5. In Appendix analogous results are given for superintuitionistic logics.
A precise measurement of the Z resonance parameters through its hadronic decays
1990
A measurement of the cross section for e+e-→ hadrons using 11 000 hadronic decays of the Z boson at ten different center-of-mass energies is presented. A three-parameter fit gives the following values for the Z mass MZ, the total width ΓZ, the product of the electronic and hadronic partial widths ΓeΓh, and the unfolded pole cross section σ0: MZ = 91.171 ± 0.030 (stat.) ± 0.030 (beam) GeV, ΓZ = 2.511 ± 0.065 GeV, ΓeΓh = 0.148 ± 0.006 (stat.) ± 0.004 (syst.) GeV2, σ0 = 41.6 ± 0.7 (stat.) ± 1.1 (syst.) nb, Good agreement with the predictions of the standard model is observed. From a two-parameter fit the number of massless neutrino generations is found to be Nv = 2.91 ± 0.26. Thus the hypothes…
Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as a Procrustean Bed for His Modal Metaphysics
2012
Even if Leibniz didn’t have the opportunity to actually conceive an explicit modal logic system, remains the fact that he had worked out a modal metaphysics, of which the inaugural act, in his Elementa juris naturalis (c. 1671) was an obvious reference to the Apulean square of opposition. Later, scholars acknowledged in this passage probably one of the first sketch of deontic logic of norms. His modal metaphysics rather deals with the so-called alethic modalities, sometimes expounded through a language such as R.M. Adams wondered whether Leibniz could be “a sort of grandfather of possible worlds semantics for modal logic”. In the following study, the Apulean square is used as a hermeneutic …
Monadic second-order logic over pictures and recognizability by tiling systems
1994
We show that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system if and only if it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and matches a natural logic. The proof is based on the Ehrenfeucht-FraIsse technique for first-order logic and an implementation of “threshold counting” within tiling systems.