497 research outputs found
Temporalized logics and automata for time granularity
Suitable extensions of the monadic second-order theory of k successors have
been proposed in the literature to capture the notion of time granularity. In
this paper, we provide the monadic second-order theories of downward unbounded
layered structures, which are infinitely refinable structures consisting of a
coarsest domain and an infinite number of finer and finer domains, and of
upward unbounded layered structures, which consist of a finest domain and an
infinite number of coarser and coarser domains, with expressively complete and
elementarily decidable temporal logic counterparts.
We obtain such a result in two steps. First, we define a new class of
combined automata, called temporalized automata, which can be proved to be the
automata-theoretic counterpart of temporalized logics, and show that relevant
properties, such as closure under Boolean operations, decidability, and
expressive equivalence with respect to temporal logics, transfer from component
automata to temporalized ones. Then, we exploit the correspondence between
temporalized logics and automata to reduce the task of finding the temporal
logic counterparts of the given theories of time granularity to the easier one
of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym:
TPLP Category: Paper for Special Issue (Verification and Computational Logic)
Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September
200
Carnap: an Open Framework for Formal Reasoning in the Browser
This paper presents an overview of Carnap, a free and open framework for the development of formal reasoning applications. Carnap’s design emphasizes flexibility, extensibility, and rapid prototyping. Carnap-based applications are written in Haskell, but can be compiled to JavaScript to run in standard web browsers. This combination of features makes Carnap ideally suited for educational applications, where ease-of-use is crucial for students and adaptability to different teaching strategies and classroom needs is crucial for instructors. The paper describes Carnap’s implementation, along with its current and projected pedagogical applications
Heap Abstractions for Static Analysis
Heap data is potentially unbounded and seemingly arbitrary. As a consequence,
unlike stack and static memory, heap memory cannot be abstracted directly in
terms of a fixed set of source variable names appearing in the program being
analysed. This makes it an interesting topic of study and there is an abundance
of literature employing heap abstractions. Although most studies have addressed
similar concerns, their formulations and formalisms often seem dissimilar and
some times even unrelated. Thus, the insights gained in one description of heap
abstraction may not directly carry over to some other description. This survey
is a result of our quest for a unifying theme in the existing descriptions of
heap abstractions. In particular, our interest lies in the abstractions and not
in the algorithms that construct them.
In our search of a unified theme, we view a heap abstraction as consisting of
two features: a heap model to represent the heap memory and a summarization
technique for bounding the heap representation. We classify the models as
storeless, store based, and hybrid. We describe various summarization
techniques based on k-limiting, allocation sites, patterns, variables, other
generic instrumentation predicates, and higher-order logics. This approach
allows us to compare the insights of a large number of seemingly dissimilar
heap abstractions and also paves way for creating new abstractions by
mix-and-match of models and summarization techniques.Comment: 49 pages, 20 figure
Modal Logic S5 Satisfiability in Answer Set Programming
Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.</p
Deciding Second-order Logics using Database Evaluation Techniques
We outline a novel technique that maps the satisfiability problems of
second-order logics, in particular WSnS (weak monadic second-order
logic with n successors), S1S (monadic second-order logic with one
successor), and of ÎĽ-calculus, to the problem of query evaluation
of Complex-value Datalog queries. In this dissertation, we propose
techniques that use database evaluation and optimization techniques
for automata-based decision procedures for the above logics. We show
how the use of advanced implementation techniques for Deductive
databases and for Logic Programs, in particular the use of tabling,
yields a considerable improvement in performance over more traditional
approaches. We also explore various optimizations of the proposed
technique, in particular we consider variants of tabling and goal
reordering. We then show that the decision problem for S1S can be
mapped to the problem of query evaluation of
Complex-value Datalog queries.
We explore optimizations that
can be applied to various types of formulas. Last, we propose
analogous techniques that allow us to approach ÎĽ-calculus
satisfiability problem in an incremental fashion and without the need
for re-computation. In addition, we outline a top-down evaluation
technique to drive our incremental procedure and propose heuristics
that guide the problem partitioning to reduce the size of the problems
that need to be solved
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
Truszczy´nski 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),
R´egion 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
Reasoning about Data Repetitions with Counter Systems
We study linear-time temporal logics interpreted over data words with
multiple attributes. We restrict the atomic formulas to equalities of attribute
values in successive positions and to repetitions of attribute values in the
future or past. We demonstrate correspondences between satisfiability problems
for logics and reachability-like decision problems for counter systems. We show
that allowing/disallowing atomic formulas expressing repetitions of values in
the past corresponds to the reachability/coverability problem in Petri nets.
This gives us 2EXPSPACE upper bounds for several satisfiability problems. We
prove matching lower bounds by reduction from a reachability problem for a
newly introduced class of counter systems. This new class is a succinct version
of vector addition systems with states in which counters are accessed via
pointers, a potentially useful feature in other contexts. We strengthen further
the correspondences between data logics and counter systems by characterizing
the complexity of fragments, extensions and variants of the logic. For
instance, we precisely characterize the relationship between the number of
attributes allowed in the logic and the number of counters needed in the
counter system.Comment: 54 page
Foundations of Object-Oriented Languages
A report on the workshop Foundations of Object-Oriented Languages, Paris, July 1994
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