The satisfiability problem for monadic infinite-valued Gödel logic is known to be undecidable. We identify a fragment of this logic extended with strong negation whose satisfiability is not only decidable but it is decidable within classical logic. We use this fragment to formalize the rules of CADIAG-2, a well performing fuzzy expert system assisting in the differential diagnosis in internal medicine. A (classical) satisfiability check of the resulting formulas allowed the detection of some errors in the rules of the system.

A plan with rich control structures like branches and loops can usually serve as a general solution that solves multiple planning instances in a domain. However, the correctness of such generalized plans is non-trivial to define and verify, especially when it comes to whether or not a plan works for all of the infinitely many instances of the problem. In this paper, we give a precise definition of a generalized plan representation called an FSA plan, with its semantics defined in the situation calculus. Based on this, we identify a class of infinite planning problems, which we call one-dimensional (1d), and prove a correctness result that 1d problems can be verified by finite means. We show that this theoretical result leads to a practical algorithm that does this verification practically, and a planner based on this verification algorithm efficiently generates provably correct plans for 1d problems.

We consider a generalized form of planning, possibly involving loops, that arises in nondeterministic domains when ex- plicit strong fairness constraints are asserted over the planning domain. Such constraints allow us to specify the necessity of occurrence of selected effects of nondeterministic actions over domain’s runs. Also they are particularly meaningful from the technical point of view because they exhibit the expressiveness advantage of LTL over CTL in verification. We show that planning for reachability and maintenance goals is EXPTIME-complete in this setting, that is, it has the same complexity as conditional planning in nondeterministic domains (without strong fairness constraints). We also show that within the EXPTIME bound one can solve the more general problems of realizing agent planning programs as well as composition-based planning in the presence of strong fairness constraints.

Measuring the inconsistency degree of a knowledge base can help us to deal with inconsistencies. Several inconsistency measures have been given under different multi-valued semantics, including 4-valued semantics, 3-valued semantics, LPm and Quasi Classical semantics. In this paper, we first carefully analyze the relationship between these inconsistency measures by showing that the inconsistency degrees under 4-valued semantics, 3-value semantics, LPm are the same, but different from the one based on Quasi Classical semantics. We then consider the computation of these inconsistency measures and show that computing inconsistency measurement under multi-valued semantics is usually intractable. To tackle this problem, we propose two novel algorithms that respectively encode the problems of computing inconsistency degrees under 4-valued semantics (3-valued semantics, LPm) and under Quasi Classical semantics into the partial Max-SAT problems. We implement these algorithms and do experiments on some benchmark data sets. The preliminary but encouraging experimental results show that our approach is efficient to handle large knowledge bases.

We provide two approaches for explaining inconsistency in multi-context systems, where decentralized and heterogeneous system parts interact via nonmonotonic bridge rules. Inconsistencies arise easily in such scenarios, and nonmonotonicity calls for specific methods of inconsistency analysis. Both our approaches characterize inconsistency in terms of involved bridge rules: either by pointing out rules which need to be altered for restoring consistency, or by finding combinations of rules which cause inconsistency. We show duality and modularity properties, give precise complexity characterizations, and provide algorithms for computation using HEX-programs. Our results form a basis for inconsistency management in heterogeneous knowledge integration systems.

In this paper, we introduce a new class of local consistencies, called df-consistencies, for qualitative constraint networks. Each consistency of this class is based on weak composition and a mapping f that provides a covering for each relation of the considered qualitative calculus. We study the connections existing between some properties of the introduced mappings and the relative inference strength of df-consistencies. The consistency obtained by the usual closure under weak composition corresponds to the weakest element of the class, whereas df-consistencies stronger than weak composition open new promising perspectives. Interestingly, the class of df-consistencies is shown to form a complete lattice where the partial order denotes the relative strength of every two consistencies. We also propose a generic algorithm that allows us to compute the closure of qualitative constraint networks under any "well-behaved" consistency of the class. The experimentation that we have conducted on qualitative constraint networks from the Interval Algebra shows the interest of these new local consistencies, in particular for the consistency problem.

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives.

We identify three classes of four-state paraconsistent logics according to their different approaches towards the disjunctive syllogism, and investigate three representatives of these approaches: Quasi-classical logic, which always accepts this principle, Belnap's logic, that rejects the disjunctive syllogism altogether, and a logic of inconsistency minimization that restricts its application to consistent fragments only. These logics are defined in a syntactic and a semantic style, which are linked by a simple transformation. It is shown that the three formalisms accommodate knowledge minimization, and that the most liberal formalism towards the disjunctive syllogism is also the strongest among the three, while the most cautious logic is the weakest one.

The DL-Lite family of Description Logics has been designed with the specific goal of allowing for answering complex queries (in particular, conjunctive queries) over ontologies with very large instance sets (ABoxes). So far, in DL-Lite systems, this goal has been actually achieved only for relatively simple (short) conjunctive queries. In this paper we present Presto, a new query answering technique for DL-Lite ontologies, and an experimental comparison of Presto with the main previous approaches to query answering in DL-Lite. In practice, our experiments show that, in real ontologies, current techniques are only able to answer conjunctive queries of less than 7-10 atoms (depending on the complexity of the TBox), while Presto is actually able to handle conjunctive queries of up to 30 atoms. Furthermore, in the cases that are already successfully handled by previous approaches, Presto is significantly more efficient.

We investigate the computational complexity of axiom pinpointing, which is the task of finding minimal subsets of a Description Logic knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used.