1,720,984 research outputs found
Completeness of a Branching-Time Logic with Possible Choices
No full textIn this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance Stit Logics. © 2010 Springer Science+Business Media B.V
Normality operators and classical recapture in many-valued logic
No full textIn this paper, we use a 'normality operator' in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some (or all) of the three properties, namely subclassicality and two properties that we call fixed-point negation property and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics K⊛3, LP⊛, Kw⊛3, PWK⊛ and Efde⊛, that are in turn extensions of K3, LP, Kw3, PWK and Efde, respectively
Inevitable ignorance as a standard for excusability: an epistemological analysis
No full textIn this paper, we discuss the notion of inevitable ignorance that the Italian Constitutional Court has introduced in justifying a restriction of the legal maxim Ignorantia legis non excusat. In particular, we argue that the epistemic flavor of the notion extends to the notion of inevitability beside that of ignorance, and we offer an epistemic analysis of the notion. This analysis is based both on the legal-theoretical framework defined by the justification of the restriction of the maxim, and on a discussion of some paradigmatic Italian cases where the standard of excusability involving inevitable ignorance is applied. The analysis reveals that the notion of inevitable ignorance is closely connected to a number of notions also used in formal epistemology, such as belief, evidence, rationality, and trust
The abundance of the future: A paraconsistent approach to future contingents
Full text linkSupervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this "abundance of the future" is a non-adjunctive paraconsistent formalism based on subvaluations, which has the virtue that all classical laws are valid in it, while no formula like φ & - φ is satisfiable (though both φ and - φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. © Nicolaus Copernicus University (Toruń) 2013
Comparing semantics for temporal STIT logic
Full text linkIn this paper we establish equivalence results for the different semantics for the temporal STIT logic T-STIT, that includes temporal operators and the group agency operator for the grand coalition, and we study a semantics for temporal STIT that is based on the concept of interpreted system à la Fagin et al. We discuss the descriptive adequacy of the above semantics in capturing a given gametheoretical scenario where information about the players is included, and we compare them with traditional BT+AC semantics. Also, we discuss the extension of T-STIT with full groups and the corresponding operators, and we discuss the distinction between frames that impose additivity and superadditivity on the choices of arbitrary groups
Conditional Doxastic Logic with Oughts and Concurrent Upgrades
No full textIn this paper, we model the behavior of an epistemic agent that faces a deliberation against a background of oughts, beliefs and information. We do this by introducing a dynamic epistemic logic where ought operators are defined and release of information makes beliefs and oughts co-vary. The static part of the logic extends single-agent Conditional Doxastic Logic by combining dyadic operators for conditional beliefs and oughts that are interpreted over two distinct preorders. The dynamic part of the logic introduces concurrent upgrade operators, which are interpreted on operations that change the two preorders in the same way, thus generating the covariation of beliefs and oughts. The effect of the covariation is that, after receiving new information, the agent will change both her beliefs and her oughts accordingly, and in deliberating, she will pick up the best states among those she takes to be the most plausible
Stit Logics, Games, Knowledge, and Freedom
No full textThis chapter has two main goals: highlighting the connections between Stit logics and game theory and comparing Stit logics with Matrix Game Logic, a Dynamic Logic introduced by van Benthem in order to model some interesting epistemic notions from game theory. Achieving the first goal will prove the flexibility of Stit logics and their applicability in the logical foundations of game theory, and will lay the groundwork for accomplishing the second. A comparison between Stit logics and Matrix Game Logic is already offered in recent work by van Benthem and Pacuit. Here, we push the comparison further by embedding Matrix Game Logic into a fragment of group Stit logic, and using the embedding to derive some properties of Matrix Game Logic—in particular, undecidability and the lack of finite axiomatizability. In addition, the embedding sheds light on some open issues about the so-called “freedom operator” of Matrix Game Logic
Logics based on linear orders of contaminating values
Full text linkA wide family of many-valued logics - for instance, those based on the weak Kleene algebra - includes a non-classical truth-value that is 'contaminating' in the sense that whenever the value is assigned to a formula , any complex formula in which $arphi appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behaviour is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper
Completeness of a Branching-Time Logic with Possible Choices
No full textIn this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance Stit Logics
Composition, Counterfactuals and Causation. Special Issue on the Philosophy of David Lewis
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