30,307 research outputs found
Transition Systems for Model Generators - A Unifying Approach
A fundamental task for propositional logic is to compute models of
propositional formulas. Programs developed for this task are called
satisfiability solvers. We show that transition systems introduced by
Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers
can be adapted for solvers developed for two other propositional formalisms:
logic programming under the answer-set semantics, and the logic PC(ID). We show
that in each case the task of computing models can be seen as "satisfiability
modulo answer-set programming," where the goal is to find a model of a theory
that also is an answer set of a certain program. The unifying perspective we
develop shows, in particular, that solvers CLASP and MINISATID are closely
related despite being developed for different formalisms, one for answer-set
programming and the latter for the logic PC(ID).Comment: 30 pages; Accepted for presentation at ICLP 2011 and for publication
in Theory and Practice of Logic Programming; contains the appendix with
proof
Mackey-complete spaces and power series -- A topological model of Differential Linear Logic
In this paper, we have described a denotational model of Intuitionist Linear
Logic which is also a differential category. Formulas are interpreted as
Mackey-complete topological vector space and linear proofs are interpreted by
bounded linear functions. So as to interpret non-linear proofs of Linear Logic,
we have used a notion of power series between Mackey-complete spaces,
generalizing the notion of entire functions in C. Finally, we have obtained a
quantitative model of Intuitionist Differential Linear Logic, where the
syntactic differentiation correspond to the usual one and where the
interpretations of proofs satisfy a Taylor expansion decomposition
Super Logic Programs
The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful
nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper,
we specialize it to a class of theories called `super logic programs'. We argue
that these programs form a natural generalization of standard logic programs.
In particular, they allow disjunctions and default negation of arbibrary
positive objective formulas.
Our main results are two new and powerful characterizations of the static
semant ics of these programs, one syntactic, and one model-theoretic. The
syntactic fixed point characterization is much simpler than the fixed point
construction of the static semantics for arbitrary AELB theories. The
model-theoretic characterization via Kripke models allows one to construct
finite representations of the inherently infinite static expansions.
Both characterizations can be used as the basis of algorithms for query
answering under the static semantics. We describe a query-answering interpreter
for super programs which we developed based on the model-theoretic
characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200
Quantifier-Free Interpolation of a Theory of Arrays
The use of interpolants in model checking is becoming an enabling technology
to allow fast and robust verification of hardware and software. The application
of encodings based on the theory of arrays, however, is limited by the
impossibility of deriving quantifier- free interpolants in general. In this
paper, we show that it is possible to obtain quantifier-free interpolants for a
Skolemized version of the extensional theory of arrays. We prove this in two
ways: (1) non-constructively, by using the model theoretic notion of
amalgamation, which is known to be equivalent to admit quantifier-free
interpolation for universal theories; and (2) constructively, by designing an
interpolating procedure, based on solving equations between array updates.
(Interestingly, rewriting techniques are used in the key steps of the solver
and its proof of correctness.) To the best of our knowledge, this is the first
successful attempt of computing quantifier- free interpolants for a variant of
the theory of arrays with extensionality
On finitely recursive programs
Disjunctive finitary programs are a class of logic programs admitting
function symbols and hence infinite domains. They have very good computational
properties, for example ground queries are decidable while in the general case
the stable model semantics is highly undecidable. In this paper we prove that a
larger class of programs, called finitely recursive programs, preserves most of
the good properties of finitary programs under the stable model semantics,
namely: (i) finitely recursive programs enjoy a compactness property; (ii)
inconsistency checking and skeptical reasoning are semidecidable; (iii)
skeptical resolution is complete for normal finitely recursive programs.
Moreover, we show how to check inconsistency and answer skeptical queries using
finite subsets of the ground program instantiation. We achieve this by
extending the splitting sequence theorem by Lifschitz and Turner: We prove that
if the input program P is finitely recursive, then the partial stable models
determined by any smooth splitting omega-sequence converge to a stable model of
P.Comment: 26 pages, Preliminary version in Proc. of ICLP 2007, Best paper awar
More on Unfold/Fold Transformations of Normal Programs: Preservation of Fitting's Semantics
The unfold/fold transformation system defined by Tamaki and Sato was meant for definite programs. It transforms a program into an equivalent one in the sense of both the least Herbrand model semantics and the Computed Answer Substitution semantics. Seki extended the method to normal programs and specialized it in order to preserve also the finite failure set. The resulting system is correct wrt nearly all the declarative semantics for normal programs. An exception is Fitting's model semantics. In this paper we consider a slight variation of Seki's method and we study its correctness wrt Fitting's semantics. We define an applicability condition for the fold operation and we show that it ensures the preservation of the considered semantics through the transformation
Transforming Normal Programs by Replacement
The replacement transformation operation, already defined in [28], is studied wrt normal programs. We give applicability conditions able to ensure the correctness of the operation wrt Fitting's and Kunen's semantics. We show how replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too. Furthermore we characterize a transformation sequence for which the preservation of Fitting's and Kunen's semantics is ensured
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