Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al.'s ProbLog and Vennekens et al.'s LPAD, is aimed at combining statistical and logical knowledge representation and inference. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a symbolic inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks.

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming of Datalog-based languages became evident, e.g. in the context of data-integration (consistent query-answering, ontology-based data access) and Semantic Web applications: The language does not permit any generation of and reasoning with unnamed individuals in an obvious way. In general, it is weak in supporting many cases of existential quantification. To overcome this problem, Datalog∃ has recently been proposed, which extends traditional Datalog by existential quantification in rule heads. In this work, we propose a natural extension of Disjunctive Datalog and Datalog∃, called Datalog∃,˅, which allows both disjunctions and existential quantification in rule heads and is therefore an attractive language for knowledge representation and reasoning, especially in domains where ontology-based reasoning is needed. We formally define syntax and semantics of the language Datalog∃,˅, and provide a notion of instantiation, which we prove to be adequate for Datalog∃,˅. A main issue of Datalog∃ and hence also of Datalog∃,˅ is that decidability is no longer guaranteed for typical reasoning tasks. In order to address this issue, we identify many decidable fragments of the language, which extend, in a natural way, analog classes defined in the non-disjunctive case. Moreover, we carry out an in-depth complexity analysis, deriving interesting results which range from Logarithmic Space to Exponential Time.

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a dictionary of words and their ASP-lambda formulas. However such an approach is not scalable. In this paper our focus is on two algorithms that allow one to construct ASP-lambda formulas in an inverse manner. In particular the two algorithms take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F such that F with input as G, denoted by F@G, is equal to H; and similarly G@F = H. We present correctness and complexity results about these algorithms. To do that we develop the notion of typed ASP-lambda calculus theories and their orders and use it in developing the completeness results.

Constraint Handling Rules (CHRs) are a high-level rule-based programming language for specification and implementation of constraint solvers. CHR manipulates a global store representing a flat conjunction of constraints. By default, CHR does not support goals with a more complex propositional structure including disjunction, negation, etc., or CHR relies on the host system to provide such features. In this paper we introduce Satisfiability Modulo Constraint Handling Rules (SMCHR): a tight integration of CHR with a modern Boolean Satisfiability (SAT) solver for quantifier-free formulae with an arbitrary propositional structure. SMCHR is essentially a Satisfiability Modulo Theories (SMT) solver where the theory T is implemented in CHR. The execution algorithm of SMCHR is based on lazy clause generation, where a new clause for the SAT solver is generated whenever a rule is applied. We shall also explore the practical aspects of building an SMCHR system, including extending a “built-in” constraint solver supporting equality with unification and justifications.

We present the hybrid ASP solver clingcon, combining the simple modeling language and the high performance Boolean solving capacities of Answer Set Programming (ASP) with techniques for using non-Boolean constraints from the area of Constraint Programming (CP). The new clingcon system features an extended syntax supporting global constraints and optimize statements for constraint variables. The major technical innovation improves the interaction between ASP and CP solver through elaborated learning techniques based on irreducible inconsistent sets. A broad empirical evaluation shows that these techniques yield a performance improvement of an order of magnitude.

We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal.

Generalized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption.

We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be modular, in the sense that they also work if applied only to part of a theory, in order to achieve a useful notion of relative expressiveness. We present simulations showing that logics in DL with and without the capability of team defeat are equally expressive. We also show that logics that handle ambiguity differently – ambiguity blocking versus ambiguity propagating – have distinct expressiveness, with neither able to simulate the other under a different formulation of expressiveness.

In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their linear variant. Compiled clauses were themselves logic formulas except for the presence of a second-order abstraction over the atomic goals matching their head. In this paper, we revisit our previous results into a more detailed and fully logical justification that does away with this spurious abstraction. We then refine the resulting technique to support well-moded programs efficiently.

Traditional approaches to automatic AND-parallelization of logic programs rely on some static analysis to identify independent goals that can be safely and efficiently run in parallel in any possible execution. In this paper, we present a novel technique for generating annotations for independent AND-parallelism that is based on partial evaluation. Basically, we augment a simple partial evaluation procedure with (run-time) groundness and variable sharing information so that parallel conjunctions are added to the residual clauses when the conditions for independence are met. In contrast to previous approaches, our partial evaluator is able to transform the source program in order to expose more opportunities for parallelism. To the best of our knowledge, we present the first approach to a parallelizing partial evaluator.

Given an elliptic curve E over a field of positive characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing algorithms and then present a new approach that exploits structural differences between ordinary and supersingular isogeny graphs. This yields a simple algorithm that, given E and a suitable non-residue in 𝔽p2, determines the supersingularity of E in O(n3log 2n) time and O(n) space, where n=O(log p) . Both these complexity bounds are significant improvements over existing methods, as we demonstrate with some practical computations.

From power series expansions of functions on curves over finite fields, one can obtain sequences with perfect or almost perfect linear complexity profile. It has been suggested by various authors to use such sequences as key streams for stream ciphers. In this work, we show how long parts of such sequences can be computed efficiently from short ones. Such sequences should therefore be considered to be cryptographically weak. Our attack leads in a natural way to a new measure of the complexity of sequences which we call expansion complexity.

The chromatic polynomial P(G,λ) gives the number of ways a graph G can be properly coloured in at most λ colours. This polynomial has been extensively studied in both combinatorics and statistical physics, but there has been little work on its algebraic properties. This paper reports a systematic study of the Galois groups of chromatic polynomials. We give a summary of the Galois groups of all chromatic polynomials of strongly non-clique-separable graphs of order at most 10 and all chromatic polynomials of non-clique-separable θ-graphs of order at most 19. Most of these chromatic polynomials have symmetric Galois groups. We give five infinite families of graphs: one of these families has chromatic polynomials with a dihedral Galois group and two of these families have chromatic polynomials with cyclic Galois groups. This includes the first known infinite family of graphs that have chromatic polynomials with the cyclic Galois group of order 3.

We prove that under any projective embedding of an abelian variety A of dimension g, a complete set of addition laws has cardinality at least g+1, generalizing a result of Bosma and Lenstra for the Weierstrass model of an elliptic curve in ℙ2. In contrast, we prove, moreover, that if k is any field with infinite absolute Galois group, then there exists for every abelian variety A/k a projective embedding and an addition law defined for every pair of k-rational points. For an abelian variety of dimension 1 or 2, we show that this embedding can be the classical Weierstrass model or the embedding in ℙ15, respectively, up to a finite number of counterexamples for ∣k∣≤5 .

Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow the hiding of irrelevant parts of the state during verification, whereas the anti-frame rule allows the hiding of local state from the context.

We discuss the semantic foundations of frame and anti-frame rules, and present the first sound model for Charguéraud and Pottier's type and capability system including both of these rules. The model is a possible worlds model based on the operational semantics and step-indexed heap relations, and the worlds are given by a recursively defined metric space. We also extend the model to account for Pottier's generalised frame and anti-frame rules, where invariants are generalised to families of invariants indexed over preorders. This generalisation enables reasoning about some well-bracketed as well as (locally) monotone uses of local state.

In this paper a new sliding mode controller for set-point control of robot manipulators is proposed. The controller does not use any part of the robot dynamics in the control law. Thus, it is structurally simpler than other sliding mode controllers where the control law uses a nominal model of the robot dynamics. The controller uses a new nonlinear Proportional-Integral-Derivative (PID) sliding surface. The stability of the controlled robot dynamics is proved. On applying the boundary-layer approach to remove chattering, a nonlinear PID controller exists inside the boundary layer. This PID controller ensures that the error tend to zero asymptotically if there is no disturbances applied to the robot dynamics.