52,901 research outputs found
The Logic of Internal Rational Agent
In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent \textbf{LRA} \cite{LRA}. We call our logic (Logic of Internal Rational Agency). In contrast to \textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic \cite{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use \textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for \textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of \textbf{LRA}, two more possibility operators for \textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for . Finally, we formalize all the truth-functional -ary extensions of the negation fragment of (including itself) as well as their basic modal extension via linear-type natural deduction systems
The Logic of Internal Rational Agent
In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent \textbf{LRA} \cite{LRA}. We call our logic (Logic of Internal Rational Agency). In contrast to \textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic \cite{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use \textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for \textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of \textbf{LRA}, two more possibility operators for \textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for . Finally, we formalize all the truth-functional -ary extensions of the negation fragment of (including itself) as well as their basic modal extension via linear-type natural deduction systems
Linear-Time Temporal Answer Set Programming
[Abstract]: In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.Xunta de Galicia; ED431B 2019/03We are thankful to the anonymous reviewers for their thorough work and their useful
suggestions that have helped to improve the paper. A special thanks goes to Mirosaw
TruszczyÂŽnski for his support in improving the quality of our paper. We are especially
grateful to David Pearce, whose help and collaboration on Equilibrium Logic was the
seed for a great part of the current paper. This work was partially supported by MICINN,
Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain (GPC ED431B 2019/03),
RÂŽegion Pays de la Loire, France, (projects EL4HC and etoiles montantes CTASP), European
Union COST action CA-17124, and DFG grants SCHA 550/11 and 15, Germany
Integrating processes in temporal logic
In this paper we propose a technique to integrate process models in
classical structures for quantified temporal (modal) logic. The idea
is that in a temporal logic processes are ordinary syntactical objects
with a specific semantical representation. So we want to achieve a
`temporal logics of processes\u27 to adequately describe aspects of
systems dealing with data structures, reactive and time-critical
behavior, environmental influences, and their interaction in a single
frame. Thus the structural information of processes can be captured
and exploited to guide proofs. As an instance of this scheme we
present a quantified, metric, linear temporal logic containing
processes and conjunctions of processes explicitly. Like a predicate a
process can be regarded as a special kind of atomic formula with its
own intension, a family of sets collecting the observable behavior as
`runs\u27. A run is comparable with a Hoare-traces or a timed
observational sequence it is a sequence of sequences of values taken
from a set of objects. Each single value can be regarded as a
snapshot of an observable feature at a moment in time, e.g. a value
transmitted through a channel. Such a set has to respects the
structure of the underlying temporal logic, but not one to one, we do
not require that for a path in the time structure there is exactly one
possible run. Since each run has a certain length, the view of a run
is in particular associated with a time interval. The difference
between moments and intervals of time is expressed by several kinds of
modal operators each of them with restrictions in the shape of
annotated equations and predicates to determined the relevant time
slices. We describe syntax and semantic of this logic especially with
a focus on the process part. Finally we sketch a calculus and give
some examples
Logics for modelling collective attitudes
We introduce a number of logics to reason about collective propositional
attitudes that are defined by means of the majority rule. It is well known that majoritarian
aggregation is subject to irrationality, as the results in social choice theory and judgment
aggregation show. The proposed logics for modelling collective attitudes are based on
a substructural propositional logic that allows for circumventing inconsistent outcomes.
Individual and collective propositional attitudes, such as beliefs, desires, obligations, are
then modelled by means of minimal modalities to ensure a number of basic principles. In
this way, a viable consistent modelling of collective attitudes is obtained
A Note on Parameterised Knowledge Operations in Temporal Logic
We consider modeling the conception of knowledge in terms of temporal logic.
The study of knowledge logical operations is originated around 1962 by
representation of knowledge and belief using modalities. Nowadays, it is very
good established area. However, we would like to look to it from a bit another
point of view, our paper models knowledge in terms of linear temporal logic
with {\em past}. We consider various versions of logical knowledge operations
which may be defined in this framework. Technically, semantics, language and
temporal knowledge logics based on our approach are constructed. Deciding
algorithms are suggested, unification in terms of this approach is commented.
This paper does not offer strong new technical outputs, instead we suggest new
approach to conception of knowledge (in terms of time).Comment: 10 page
Non-normal modalities in variants of Linear Logic
This article presents modal versions of resource-conscious logics. We
concentrate on extensions of variants of Linear Logic with one minimal
non-normal modality. In earlier work, where we investigated agency in
multi-agent systems, we have shown that the results scale up to logics with
multiple non-minimal modalities. Here, we start with the language of
propositional intuitionistic Linear Logic without the additive disjunction, to
which we add a modality. We provide an interpretation of this language on a
class of Kripke resource models extended with a neighbourhood function: modal
Kripke resource models. We propose a Hilbert-style axiomatization and a
Gentzen-style sequent calculus. We show that the proof theories are sound and
complete with respect to the class of modal Kripke resource models. We show
that the sequent calculus admits cut elimination and that proof-search is in
PSPACE. We then show how to extend the results when non-commutative connectives
are added to the language. Finally, we put the logical framework to use by
instantiating it as logics of agency. In particular, we propose a logic to
reason about the resource-sensitive use of artefacts and illustrate it with a
variety of examples
Reasoning about Knowledge in Linear Logic: Modalities and Complexity
In a recent paper, Jean-Yves Girard commented that âit has been a long time since philosophy has stopped intereacting with logicâ[17]. Actually, it has no
Categoricity and Possibility. A Note on Williamson's Modal Monism
The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic
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