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PTL: A Propositional Typicality Logic [chapter]

Richard Booth, Thomas Meyer, Ivan Varzinczak
2012 Lecture Notes in Computer Science  
We introduce 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').  ... 
doi:10.1007/978-3-642-33353-8_9 fatcat:mwucomtwcfe3vcp7nwaqa34bui

A Propositional Typicality Logic for Extending Rational Consequence

Richard Booth, Thomas Meyer, Ivan Varzinczak
2012 Proceedings of the 13th European Conference on Logics in Artificial Intelligence   unpublished
We introduce 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).  ... 
fatcat:fo5tdiyxknhl5kptlk4hi5ahqq

What Does Entailment for PTL Mean?

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
unpublished
We do so in the framework of Propo-sitional 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.  ... 
fatcat:26nytjdcofcvxmxy2pn6cjhzp4

On rational entailment for propositional typicality logic

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
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.  ... 
doi:10.1016/j.artint.2019.103178 fatcat:6wtakpxhyza2bomgyllnpqxoka

On Rational Entailment for Propositional Typicality Logic [article]

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
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.  ... 
arXiv:1809.10946v1 fatcat:ie4gy5swkfg7jarmrwcc2l67oi

Defeasibility applied to Forrester's paradox

Julian Chingoma, Thomas Meyer
2020 South African Computer Journal  
KLM-style defeasible reasoning is 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) .  ... 
doi:10.18489/sacj.v32i2.848 fatcat:xhdsvkxy6jfcrdoethrnmjgfca

Is There a Future for Deductive Temporal Verification?

C. Dixon, M. Fisher, B. Konev
2006 Thirteenth International Symposium on Temporal Representation and Reasoning (TIME'06)  
In this paper, we consider 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.  ... 
doi:10.1109/time.2006.19 dblp:conf/time/DixonFK06 fatcat:wwczidgbjncz5odkqhlht65v3a

A Hierarchical Analysis of Propositional Temporal Logic Based on Intervals [article]

Ben Moszkowski
2006 arXiv   pre-print
We present 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.  ... 
arXiv:cs/0601008v2 fatcat:gdpsuxxhk5bfjobq3qcsicawye

An Expressive Probabilistic Temporal Logic [article]

Bruno Woltzenlogel Paleo
2017 arXiv   pre-print
The 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.  ... 
arXiv:1603.07453v2 fatcat:h22oroof6rh6bhwwqvsax4der4

Can message buffers be axiomatized in linear temporal logic?

A.P. Sistla, E.M. Clarke, N. Francez, A.R. Meyer
1984 Information and Control  
We show that all bounded buffers are characterizable in 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 (  ... 
doi:10.1016/s0019-9958(84)80043-1 fatcat:t7tbrc3hgbh3rjvjm3foipnyxu

A Hierarchical Completeness Proof for Propositional Temporal Logic [chapter]

Ben Moszkowski
2003 Lecture Notes in Computer Science  
We present 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.  ... 
doi:10.1007/978-3-540-39910-0_22 fatcat:wmsixcfdcnfljpens4gs7kya4q

Trace consistency and inevitability [chapter]

R. Ramanujam
1996 Lecture Notes in Computer Science  
Formulas of the 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.  ... 
doi:10.1007/3-540-62034-6_54 fatcat:clua36ifgjahnkziluhkfy3f5y

A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time [article]

Ben Moszkowski
2012 arXiv   pre-print
Our completeness proof uses 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.  ... 
arXiv:1207.3816v1 fatcat:z4he73ipszesjnwec2ncmebpje

Real-Time Logics: Complexity and Expressiveness

R. Alur, T.A. Henzinger
1993 Information and Computation  
Formulas of the 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] ).  ... 
doi:10.1006/inco.1993.1025 fatcat:mifm3xsdfzelzi4ja5bf4eusbq

Using Temporal Logic to Analyse Temporal Logic: A Hierarchical Approach Based on Intervals

B. Moszkowski
2007 Journal of Logic and Computation  
We present 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).  ... 
doi:10.1093/logcom/exm006 fatcat:rrg22v7ekref7jslw2gbwd3goi
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