Results 1  10
of
11
Maximal decidable fragments of Halpern and Shoham’s modal logic of intervals
, 2010
"... Abstract. In this paper, we focus our attention on the fragment of Halpern and Shoham’s modal logic of intervals (HS) that features four modal operators corresponding to the relations “meets”, “met by”, “begun by”, and “begins ” of Allen’s interval algebra (AĀBB ̄ logic). AĀBB̄ properly extends i ..."
Abstract

Cited by 14 (10 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we focus our attention on the fragment of Halpern and Shoham’s modal logic of intervals (HS) that features four modal operators corresponding to the relations “meets”, “met by”, “begun by”, and “begins ” of Allen’s interval algebra (AĀBB ̄ logic). AĀBB̄ properly extends interesting interval temporal logics recently investigated in the literature, such as the logic BB ̄ of Allen’s “begun by/begins ” relations and propositional neighborhood logic AĀ, in its many variants (including metric ones). We prove that the satisfiability problem for AĀBB̄, interpreted over finite linear orders, is decidable, but not primitive recursive (as a matter of fact, AĀBB ̄ turns out to be maximal with respect to decidability). Then, we show that it becomes undecidable when AĀBB ̄ is interpreted over classes of linear orders that contains at least one linear order with an infinitely ascending sequence, thus including the natural time flows N, Z, and R. 1
Expressive Completeness of Separation Logic With Two Variables and No Separating Conjunction ∗
"... We show that firstorder separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak secondorder logic, substantially sharpening a previous result. Capturing weak secondorder logic with such a restricted form ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
We show that firstorder separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak secondorder logic, substantially sharpening a previous result. Capturing weak secondorder logic with such a restricted form of separation logic requires substantial updates to known proof techniques. We develop these, and as a byproduct identify the smallest fragment of separation logic known to be undecidable: firstorder separation logic with one record field, two variables, and no separating conjunction.
Crossing the undecidability border with extensions of propositional neighborhood logic over natural numbers
 Journal of Universal Computer Science
"... Abstract: Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen’s relations, meets and met by). Recently, it has been shown that PNL interp ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract: Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen’s relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natural numbers, is decidable (NEXPTIMEcomplete) and that some of its natural extensions preserve decidability. Most notably, this is the case with PNL over natural numbers extended with a limited form of metric constraints and with the future fragment of PNL extended with modal operators corresponding to Allen’s relations begins, begun by, and before. This paper aims at demonstrating that PNL and its metric version MPNL, interpreted over natural numbers, are indeed very close to the border with undecidability, and even relatively weak extensions of them become undecidable. In particular, we show that (i) the addition of binders on integer variables ranging over interval lengths makes the resulting hybrid extension of MPNL undecidable, and (ii) a very weak firstorder extension of the future fragment of PNL, obtained by replacing proposition letters by a restricted subclass of firstorder formulae where only one variable is allowed, is undecidable (in contrast with the decidability of similar firstorder extensions of pointbased temporal logics).
I T L: J
"... We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at inte ..."
Abstract
 Add to MetaCart
(Show Context)
We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at intervals rather than points and the main effect of that semantic feature is substantially higher expressiveness and computational complexity of the interval logics as compared to pointbased ones. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in it over the past 10 years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of interval logics. 1
Interval Temporal Logics:a Journey
"... We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at interv ..."
Abstract
 Add to MetaCart
(Show Context)
We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at intervals rather than points and the main effect of that semantic feature is substantially higher expressiveness and computational complexity of the interval logics as compared to pointbased ones. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in it over the past 10 years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of interval logics. 1
I T L: J
"... We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at inte ..."
Abstract
 Add to MetaCart
(Show Context)
We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at intervals rather than points and the main effect of that semantic feature is substantially higher expressiveness and computational complexity of the interval logics as compared to pointbased ones. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in it over the past 10 years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of interval logics. 1
unknown title
"... Undecidability and temporal logic: some landmarks from Turing to the present (Extended abstract) ..."
Abstract
 Add to MetaCart
(Show Context)
Undecidability and temporal logic: some landmarks from Turing to the present (Extended abstract)
Hybrid Metric Propositional Neighborhood Logics with Interval Length Binders
"... We investigate the question of how much hybrid machinery can be added to the interval neighbourhood logic PNL and its metric extension MPNL without losing the decidability of their satisfiability problem in N. In particular, we consider the natural hybrid extension of MPNL obtained by adding binders ..."
Abstract
 Add to MetaCart
(Show Context)
We investigate the question of how much hybrid machinery can be added to the interval neighbourhood logic PNL and its metric extension MPNL without losing the decidability of their satisfiability problem in N. In particular, we consider the natural hybrid extension of MPNL obtained by adding binders on integer variables ranging over lengths of intervals, thus enabling storage of the length of the current interval and further references to it. We show that even a very weak natural fragment of such extensions becomes undecidable, which is somewhat surprising, being in contrast with the decidability of MPNL, which can be seen as a hybrid language with length constraints only involving constants over interval lengths. These results show that MPNL itself is, in this sense, a maximal decidable (weakly) hybrid extension of PNL.
Separation Logics and Modalities: A Survey
 JOURNAL OF APPLIED NONCLASSICAL LOGICS
, 2015
"... Like modal logic, temporal logic, or description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoarestyle proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is oft ..."
Abstract
 Add to MetaCart
Like modal logic, temporal logic, or description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoarestyle proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we propose a selection of landmark results about decidability, complexity and expressive power.