Decidability properties for fragments of CHR

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity >0). Both languages allow the use of the = built-in in the body of rules, thus are built on a host language that supports unification. However each imposes one further restriction. The first CHR dialect allows only range-restricted rules, that is, it does not allow the use of variables in the body or in the guard of a rule if they do not appear in the head. We show that the existence of an infinite computation is decidable for this dialect. The second dialect instead limits the number of atoms in the head of rules to one. We prove that in this case, the existence of a terminating computation is decidable. These results show that both dialects are strictly less expressive than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines

The State of Utah v. Joshua Jacob St. Clair : Brief of Appellant

APPEAL FROM JUDGMENT, SENTENCE (COMMITMENT) OF THIRD JUDICIAL DISTRICT COURT OF TOOELE COUNTY HONORABLE JOHN A. ROKIC

Improving the Outcome of a Probabilistic Logic Music System Generator by Using Perlin Noise

APOPCALEAPS is a logic-based music generation program that uses high level probabilistic rules. The music produced by APOPCALEAPS is controlled by parameters that can be customized by a user to create personalized songs. Perlin noise is a type of gradient noise algorithm which generates smooth and controllable variations of random numbers. This paper introduces the idea of using a Perlin noise algorithm on songs produced by APOPCALEAPS to alter their melody. The noise system modifies the song’s melody with noise values that fluctuate as measures change in a song. Songs with more notes and more elaborate differences between the notes are modified by the system more than simpler songs. The output of the system is a different but similar song. This research can be used for generation of music with structure where one would need to generate variants on a theme

CHR(PRISM)-based Probabilistic Logic Learning

PRISM is an extension of Prolog with probabilistic predicates and built-in support for expectation-maximization learning. Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. In this paper, we introduce a new probabilistic logic formalism, called CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level rapid prototyping of complex statistical models by means of "chance rules". The underlying PRISM system can then be used for several probabilistic inference tasks, including probability computation and parameter learning. We define the CHRiSM language in terms of syntax and operational semantics, and illustrate it with examples. We define the notion of ambiguous programs and define a distribution semantics for unambiguous programs. Next, we describe an implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between CHRiSM and other probabilistic logic programming languages, in particular PCHR. Finally we identify potential application domains

Confluence and Convergence in Probabilistically Terminating Reduction Systems

Convergence of an abstract reduction system (ARS) is the property that any derivation from an initial state will end in the same final state, a.k.a. normal form. We generalize this for probabilistic ARS as almost-sure convergence, meaning that the normal form is reached with probability one, even if diverging derivations may exist. We show and exemplify properties that can be used for proving almost-sure convergence of probabilistic ARS, generalizing known results from ARS.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Optimizing Compilation and Computational Complexity of Constraint Handling Rules

Constraint Handling Rules [1, 2] is a high-level programming language extension based on multi-headed committed-choice multiset rewrite rules. It can be used as a stand-alone language or as an extension to an existing host language. CHR systems have been implemented for nearly every Prolog system, and there ar