We address the problem of supporting empirical probabilities in monadic logic databases. Though the semantics of multivalued logic programs has been studied extensively, the treatment of probabilities as results of sta tistical findings has not been studied in logic programming/deductive databases. We develop a model-theoretic characterization of logic databases that facilitates such a treatment. We present an algorithm for checking consistency of such databases and prove its total correctness. We develop a sound and complete query processing procedure for handling queries to such databases.

Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical formulas. Uncertain information is expressed by means of parameterized modal operators. We propose a semantics for this multimodal logic and give a sound and complete axiomatization. We study the links with related approaches and suggest how this framework might be used to manage both uncertain and incomplere knowledge.

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is particularly investigated. Flat knowledge bases, i.e. without any priority between their elements, as well as prioritized ones where some elements are considered as more strongly entrenched than others are studied under different consequence relations. Lastly a paraconsistent-like treatment of prioritized knowledge bases is proposed, where both the level of entrenchment and the level of paraconsistency attached to a formula are propagated. The priority levels are handled in the framework of possibility theory.

In the terminology of computer science, Concurrent Systems identify systems, either software, hardware or even biological systems, where sets of activities run in parallel with possible occasional interactions. A simple example of concurrent system is the Internet, which can be thought of as a set of computers, each one computing its independent activity, that often communicate to exchange some information. A further example is the railway system of a country, where many trains travel sharing tracks in an ordered way so that two trains can move at the same time along different tracks, whereas a single track (e.g, a platform in a train station) can only be used by a single train at a time. Furthermore, the large number of activities carried on by a single human cell form a biological concurrent system, that actually shares a number of similarities with the Internet. Compared to sequential systems, where a single action is executed at a time according to a sequential algorithm, concurrent systems raise new complex issues dealing with the ordering of action executions.

Negation as failure and incomplete information in logic programs have been studied by many researchers, mainly because of their role in the foundations of declarative reading of logic programming. This paper gives a review of some of the definitions of the concepts related to of the declarative reading of logic programming. Then, the paper provides a framework to overcome misleads and to solve a misleading case study. The paper begins with reviewing the relevant work of contributions to logic programming emphasizing many concepts such as negation as failure, closed world assumption, incomplete information, and their consequences (Section 2). Then we comment on the standard definitions of the relevant logic programming concepts such as: compound terms, substitution, common instance, facts, rules, reduction, variables quantification, unifier, Most General Unifier (MGU), computation, and structured data (Section 3). Then we briefly discuss the semantics of logic programming. A logic program can have many semantics according the point of view. The common semantics are operational, denotational, and declarative (Section 4).

We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty and tradeoffs, or provide languages and algorithms that are too complex for this task. The proposed model provides a language based on rules, a semantics based on high probabilities and lexicographical preferences, and a transparent decision procedure where reasons for and against decisions interact. The model is no substitude for Decision Theory, yet for decisions that people find easy to explain it may provide an appealing alternative.

Default logic encounters some conceptual difficulties in representing common sense reasoning tasks. We argue that we should not try to formulate modular default rules that are presumed to work in all or most circumstances. We need to take into account the importance of the context which is continuously evolving during the reasoning process. Sequential thresholding is a quantitative counterpart of default logic which makes explicit the role context plays in the construction of a non-monotonic extension. We present a semantic characterization of generic non-monotonic reasoning, as well as the instantiations pertaining to default logic and sequential thresholding. This provides a link between the two mechanisms as well as a way to integrate the two that can be beneficial to both.

Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be unioned into one distributed ontology, sharable by all users without the need for prior negotiation or the development of a "standard" ontology for each field. Moreover, class algebra produces a functional correspondence between a class's class algebraic definition (i.e. its "intent") and the set of all instances which satisfy the expression (i.e. its "extent"). The framework thus provides assistance in quickly locating examples and counterexamples of various definitions. This kind of information is very valuable when developing models of the real world, and serves as an invaluable tool assisting in the proof of theorems concerning these class algebra expressions. Finally, the relative frequencies of objects in the ISA hierarchy can produce a useful Boolean algebra of probabilities. The probabilities can be used by traditional information-theoretic classification methodologies to obtain optimal ways of classifying objects in the database.

This volume contains the papers presented at CICLOPS'12: 12th International Colloquium on Implementation of Constraint and LOgic Programming Systems held on Tueseday September 4th, 2012 in Budapest. The program included 1 invited talk, 9 technical presentations and a panel discussion on Prolog open standards (open.pl). Each programme paper was reviewed by 3 reviewers. CICLOPS'12 continues a tradition of successful workshops on Implementations of Logic Programming Systems, previously held in Budapest (1993) and Ithaca (1994), the Compulog Net workshops on Parallelism and Implementation Technologies held in Madrid (1993 and 1994), Utrecht (1995) and Bonn (1996), the Workshop on Parallelism and Implementation Technology for (Constraint) Logic Programming Languages held in Port Jefferson (1997), Manchester (1998), Las Cruces (1999), and London (2000), and more recently the Colloquium on Implementation of Constraint and LOgic Programming Systems in Paphos (2001), Copenhagen (2002), Mumbai (2003), Saint Malo (2004), Sitges (2005), Seattle (2006), Porto (2007), Udine (2008), Pasadena (2009), Edinburgh (2010) - together with WLPE, Lexington (2011). We would like to thank all the authors, Tom Schrijvers for his invited talk, the programme committee members, and the ICLP 2012 organisers. We would like to also thank arXiv.org for providing permanent hosting.