1,116 research outputs found
Admissible inference rules in the linear logic of knowledge and time LTK
No full textThe paper investigates admissible inference rules for the multi-modal logic LTK, which describes a combination of linear time and knowledge. This logic is semantically defined as the set of all LTK-valid formulae, where LTK-frames are multi-modal Kripke-frames combining a linear and discrete representation of the flow of time with special S5-like modalities, defined at each time cluster and representing knowledge. We start by revising the effective finite model property in this particular case, while the central part of the paper is devoted to constructing special n-characterising models for LTK. Such structeres allow us to find an algorithm determining admissible inference rules in LTK; the main result of this work is that LTK is decidable with respect to inference rules. © Copyright 2006 Oxford University Press
Variants of multi-relational semantics for propositional non-normal modal logics
No full textA number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical systems and N-monotonic systems
Quantification in Some Non-normal Modal Logics
No full textThis paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems by Stolpe (Logic Journal of the IGPL11(5), 557–575, 2003), but unfortunately that work used only models and not frames
An axiomatisation for the multi-modal logic of knowledge and linear time LTK
No full textThe paper aims at providing the multi-modal propositional logic LTK with a sound and complete axiomatisation. This logic combines temporal and epistemic operators and focuses on m odeling the behaviour of a set of agents operating in a system on the background of a temporal framework. Time is represented as linear and discrete, whereas knowledge is modeled as an S5-like modality. A further modal operator intended to represent environment knowledge is added to the system in order to achieve the expressive power sufficient to describe the piece of information available to the agents at each moment in the flow of time
Sequence Semantics for Modelling Reason-based Preferences
No full textWe study how the non-classical n-ary operator ⊗, originally intended to capture the concept of reparative obligation, can be used in the context of social choice theory to model preferences. A novel possible-world model-theoretic semantics, called sequence semantics, was proposed for the operator. In this paper, we propose a sound and complete axiomatisation of a minimal modal logic for the operator, and we extend it with axioms suitable to model social choice consistency principles such as extension consistency and contraction consistency. We provide completeness results for such extensions.Full Tex
A Preference-based Semantics for CTD Reasoning
No full textAbstract. In [1] the authors developed a logical system based on the definition of a new non-classical connective ⊗ capturing the notion of reparative obligation. The system proved to be appropriate for handling well-known contrary-to-duty paradoxes but no model-theoretic semantics was presented. In this paper we fill the gap and define a suitable possible-world semantics for the system for which we can prove soundness and completeness. The semantics is a preference-based non-normal one extending and generalizing semantics for classical modal logics.
Legal responsibility for the acts of others: A logical analysis
No full textThis paper offers a logical analysis of two cases where legal responsibility may emerge for the acts of others: (a) reflex responsibility, and (b) responsibility in the negotiorum gestio doctrine. The current contribution works within a fresh multi-modal system where the new operators are introduced for denoting intentions and actions in the interest of other agents, and the objectively ideal sets of actions for agents
Sequence Semantics for Normative Agents
No full textWe proposed a novel framework for the representation of goals and other mental-like attitudes in terms of degree of expected outcomes, where an outcome is an order of possible alternatives. The sequences of alternatives is modelled by a non-classical (substructural) operator. In this paper we provide a modal logic based axiomatisation of the intuition they propose, and we discuss some variants (in particular for the notion of social intention, intentions that are compliant with norms). Given that the outcome operator is substructural, we first propose a novel sequence semantics (a generalisation of possible world semantics) to model the outcome operator, and we prove that the axiomatisation is sound and complete with respect to the new semantics
Sequence Semantics for Norms and Obligations
No full textThis paper presents a new version of the sequence semantics presented at DEON 2014. This new version allows us for a capturing the distinction between logic of obligations and logic of norms. Several axiom schemata are discussed, while soundness and completeness results are proved
God’s Omniscience: A Formal Analysis in Normal and Non-normal Epistemic Logics
No full textThis paper is intended to be an investigation for clarifying what it means for God to be omniscient within the realm of formal epistemic propositional logic. Assuming the validity of the Classical Propositional Calculus with its rules and laws, we shall borrow the tools of modal logics in order to describe and define the concept of Divine Knowledge. We shall try to proceed analytically, step by step, adding exactly those schemata and rules which are better suited to approximate the infinite understanding and knowledge traditionally attributed in Christianity to God
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