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PTL: A Propositional Typicality Logic
[chapter]

2012
*
Lecture Notes in Computer Science
*

We introduce

doi:10.1007/978-3-642-33353-8_9
fatcat:mwucomtwcfe3vcp7nwaqa34bui
*Propositional**Typicality**Logic*(*PTL*),*a**logic*for reasoning about*typicality*. ... We do so by enriching classical*propositional**logic*with*a**typicality*operator of which the intuition is to capture the most*typical*(or normal) situations in which*a*formula holds. ...*Propositional**Typicality**Logic*We introduce now*a**propositional**typicality**logic*, called*PTL*, which extends*propositional**logic*with*a**typicality*operator*a*(read 'bar'). ...##
###
A Propositional Typicality Logic for Extending Rational Consequence

2012
*
Proceedings of the 13th European Conference on Logics in Artificial Intelligence
*
unpublished

We introduce

fatcat:fo5tdiyxknhl5kptlk4hi5ahqq
*Propositional**Typicality**Logic*(*PTL*),*a**logic*for reasoning about*typicality*. ... We do so by enriching classical proposi-tional*logic*with*a**typicality*operator of which the intuition is to capture the most*typical*(or normal) situations in which*a*given formula holds. ... We then define and investigate*PTL*,*a**propositional**typicality**logic*extending*propositional**logic*(Sec-tion 3). ...##
###
What Does Entailment for PTL Mean?

unpublished

We do so in the framework of Propo-sitional

fatcat:26nytjdcofcvxmxy2pn6cjhzp4
*Typicality**Logic*(*PTL*), which is obtained by enriching classical*propositional**logic*with*a**typicality*operator and characterized by*a*preferential semanticsàsemantics'semanticsà ... In this paper we study different notions of entailment for*PTL*. We take as*a*starting point the notion of Rational Closure defined for KLM-style conditionals. ... Introduction*Propositional**Typicality**Logic*(*PTL*) (Booth, Meyer, and Varzinczak 2012; ) is*a*recently proposed*logic*allowing for the representation of and reasoning with*a*notion of*typicality*. ...##
###
On rational entailment for propositional typicality logic

2019
*
Artificial Intelligence
*

*Propositional*

*Typicality*

*Logic*(

*PTL*) is

*a*recently proposed

*logic*, obtained by enriching classical

*propositional*

*logic*with

*a*

*typicality*operator capturing the most

*typical*(alias normal or conventional ... Our first important result is an impossibility theorem showing that

*a*set of proposed postulates that at first all seem appropriate for

*a*notion of entailment with regard to

*typicality*cannot be satisfied ...

*Propositional*

*Typicality*

*Logic*

*PTL*[1] is

*a*

*logical*formalism explicitly allowing for the representation of and reasoning about

*a*notion of

*typicality*. ...

##
###
On Rational Entailment for Propositional Typicality Logic
[article]

2018
*
arXiv
*
pre-print

*Propositional*

*Typicality*

*Logic*(

*PTL*) is

*a*recently proposed

*logic*, obtained by enriching classical

*propositional*

*logic*with

*a*

*typicality*operator capturing the most

*typical*(alias normal or conventional ... Our first important result is an impossibility theorem showing that

*a*set of proposed postulates that at first all seem appropriate for

*a*notion of entailment with regard to

*typicality*cannot be satisfied ...

*Propositional*

*Typicality*

*Logic*

*PTL*[2] is

*a*

*logical*formalism explicitly allowing for the representation of and reasoning about

*a*notion of

*typicality*. ...

##
###
Defeasibility applied to Forrester's paradox

2020
*
South African Computer Journal
*

KLM-style defeasible reasoning is

doi:10.18489/sacj.v32i2.848
fatcat:xhdsvkxy6jfcrdoethrnmjgfca
*a**logic*system that employs defeasibility while*Propositional**Typicality**Logic*(*PTL*) is*a**logic*that does the same for the notion of*typicality*. ... This motivates the enrichment of deontic*logic*with not only the notion of defeasibility, which allows for reasoning about exceptions, but*a*stronger notion of*typicality*that is based on defeasibility ...*Typicality*is based on defeasibility and is*a*notion used in*Propositional**Typicality**Logic*(*PTL*) where its extra expressivity makes it*a*more powerful version of defeasibility (Booth et al., 2015) . ...##
###
Is There a Future for Deductive Temporal Verification?

2006
*
Thirteenth International Symposium on Temporal Representation and Reasoning (TIME'06)
*

In this paper, we consider

doi:10.1109/time.2006.19
dblp:conf/time/DixonFK06
fatcat:wwczidgbjncz5odkqhlht65v3a
*a*tractable sub-class of*propositional*linear time temporal*logic*, and provide*a*complete clausal resolution calculus for it. ... Thus, we also discuss how such*a**logic*might form the basis for practical deductive temporal verification. ... Syntax of*PTL*Semantics of*PTL*As discussed above,*a*sequence of distinct "moments" in time underlie*PTL*.*Typically*, the Natural Numbers, I , is used to represent these moments in time. ...##
###
A Hierarchical Analysis of Propositional Temporal Logic Based on Intervals
[article]

2006
*
arXiv
*
pre-print

We present

arXiv:cs/0601008v2
fatcat:gdpsuxxhk5bfjobq3qcsicawye
*a*hierarchical framework for analysing*propositional*linear-time temporal*logic*(*PTL*) to obtain standard results such as*a*small model property, decision procedures and axiomatic completeness ... Steps involved are expressed in*Propositional*Interval Temporal*Logic*(PITL) which is better suited than*PTL*for sequentially combining and decomposing formulas. ... in conventional*propositional**logic*. ...##
###
An Expressive Probabilistic Temporal Logic
[article]

2017
*
arXiv
*
pre-print

The

arXiv:1603.07453v2
fatcat:h22oroof6rh6bhwwqvsax4der4
*logic*is modal and higher-order: modalities annotated by actions are used to express possibility and necessity of*propositions*in the next states resulting from the actions, and*a*higher-order function ... This paper argues that*a*combined treatment of probabilities, time and actions is essential for an appropriate*logical*account of the notion of probability; and, based on this intuition, describes an expressive ... Finally, in contrast to the*logics*from [1] ,*PTL*requires numerical reasoning. ...##
###
Can message buffers be axiomatized in linear temporal logic?

1984
*
Information and Control
*

We show that all bounded buffers are characterizable in

doi:10.1016/s0019-9958(84)80043-1
fatcat:t7tbrc3hgbh3rjvjm3foipnyxu
*propositional*temporal*logic*(*PTL*) and so are axiomatizable. ... in Message passing is one of the primary modes of interprocess communication in*a*distributed system. ... LINEAR TEMPORAL*LOGIC*The language of*PTL*uses certain symbols called atomic*propositions*drawn from*a*finite set N, the*propositional*connectives*A*, ~, and the temporal modalities X ("next-time"), U ( ...##
###
A Hierarchical Completeness Proof for Propositional Temporal Logic
[chapter]

2003
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-540-39910-0_22
fatcat:wmsixcfdcnfljpens4gs7kya4q
*a*new proof of axiomatic completeness for*Proposition*Temporal*Logic*(*PTL*) for discrete, linear time for both finite and infinite time (without past-time). ... This makes use of*a*natural hierarchy of*logics*and notions and is an interesting alternative to the proofs in the literature based on tableaux, filtration, game theory and other methods. ... Acknowledgements The author thanks Antonio Cau and Jordan Dimitrov for comments on*a*draft version of this work. ...##
###
Trace consistency and inevitability
[chapter]

1996
*
Lecture Notes in Computer Science
*

Formulas of the

doi:10.1007/3-540-62034-6_54
fatcat:clua36ifgjahnkziluhkfy3f5y
*propositional*temporal*logic*of linear time (*PTL*) are said to be trace consistent when they cannot distinguish between equivalent runs. ... However, for*a*subclass of formulas termed coherent (*propositions*in them can be*a*ected by either of*a*pair of independent operations but not both), inevitability becomes decidable. ...*A*synopsis The*Propositional*Temporal*Logic*of Linear Time (*PTL*) is used to describe the temporal evolution of global states of distributed systems. ...##
###
A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
[article]

2012
*
arXiv
*
pre-print

Our completeness proof uses

arXiv:1207.3816v1
fatcat:z4he73ipszesjnwec2ncmebpje
*a*reduction to completeness for PITL with finite time and conventional*propositional*linear-time temporal*logic*. ... We solve the longstanding open problem of finding*a*complete axiom system for basic quantifier-free*propositional*ITL (PITL) with infinite time for analysing nonterminating computational systems. ... Dynamic Linear Time Temporal*Logic*combines*PTL*and*Propositional*Dynamic*Logic*(PDL) [FL79, HKT00] in*a*linear-time framework with infinite time. ...##
###
Real-Time Logics: Complexity and Expressiveness

1993
*
Information and Computation
*

Formulas of the

doi:10.1006/inco.1993.1025
fatcat:mifm3xsdfzelzi4ja5bf4eusbq
*propositional*linear temporal*logic**PTL*can be faithfully translated into C, by replacing*propositions*with monadic predicates. ... Introduction Linear*propositional*temporal*logic*(*PTL*) has been demonstrated to be*a*working tool for the specification and verification of reactive systems ( [Pn77] , [OL82] , [LP84] , [MP89] ). ...##
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Using Temporal Logic to Analyse Temporal Logic: A Hierarchical Approach Based on Intervals

2007
*
Journal of Logic and Computation
*

We present

doi:10.1093/logcom/exm006
fatcat:rrg22v7ekref7jslw2gbwd3goi
*a*novel way to apply temporal*logic*to the study of*a*version of itself, namely,*propositional*linear-time temporal*logic*(*PTL*). ...*A*large number of the steps involved are expressed in*a**propositional*version of Interval Temporal*Logic*(ITL) which is referred to as PITL. ... We present*a*novel way to apply temporal*logic*to the study of*a*version of itself, namely,*propositional*linear-time temporal*logic*(*PTL*). ...
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