In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.

In this article, we work towards the goal of developing agents that can learn to act in complex worlds. We develop a probabilistic, relational planning rule representation that compactly models noisy, nondeterministic action effects, and show how such rules can be effectively learned. Through experiments in simple planning domains and a 3D simulated blocks world with realistic physics, we demonstrate that this learning algorithm allows agents to effectively model world dynamics.

We present in this paper a first-order axiomatization of an extended theory $T$ of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation $\fini(t)$ which enables to distinguish between finite or infinite trees. We show that $T$ has at least one model and prove its completeness by giving not only a decision procedure, but a full first-order constraint solver which gives clear and explicit solutions for any first-order constraint satisfaction problem in $T$. The solver is given in the form of 16 rewriting rules which transform any first-order constraint $\phi$ into an equivalent disjunction $\phi$ of simple formulas such that $\phi$ is either the formula $\true$ or the formula $\false$ or a formula having at least one free variable, being equivalent neither to $\true$ nor to $\false$ and where the solutions of the free variables are expressed in a clear and explicit way. The correctness of our rules implies the completeness of $T$. We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable theories.

Representing and reasoning about qualitative temporal information is an essential part of many artificial intelligence tasks. Lots of models have been proposed in the litterature for representing such temporal information. All derive from a point-based or an interval-based framework. One fundamental reasoning task that arises in applications of these frameworks is given by the following scheme: given possibly indefinite and incomplete knowledge of the binary relationships between some temporal objects, find the consistent scenarii between all these objects. All these models require transitive tables -- or similarly inference rules-- for solving such tasks. We have defined an alternative model, S-languages - to represent qualitative temporal information, based on the only two relations of \emph{precedence} and \emph{simultaneity}. In this paper, we show how this model enables to avoid transitive tables or inference rules to handle this kind of problem.

This paper considers the problem of reasoning on massive amounts of (possibly distributed) data. Presently, existing proposals show some limitations: {\em (i)} the quantity of data that can be handled contemporarily is limited, due to the fact that reasoning is generally carried out in main-memory; {\em (ii)} the interaction with external (and independent) DBMSs is not trivial and, in several cases, not allowed at all; {\em (iii)} the efficiency of present implementations is still not sufficient for their utilization in complex reasoning tasks involving massive amounts of data. This paper provides a contribution in this setting; it presents a new system, called DLV$^{DB}$, which aims to solve these problems. Moreover, the paper reports the results of a thorough experimental analysis we have carried out for comparing our system with several state-of-the-art systems (both logic and databases) on some classical deductive problems; the other tested systems are: LDL++, XSB, Smodels and three top-level commercial DBMSs. DLV$^{DB}$ significantly outperforms even the commercial Database Systems on recursive queries. To appear in Theory and Practice of Logic Programming (TPLP)

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules.

The SNePS knowledge representation, reasoning, and acting system has several features that facilitate metacognition in SNePS-based agents. The most prominent is the fact that propositions are represented in SNePS as terms rather than as sentences, so that propositions can occur as argu- ments of propositions and other expressions without leaving first-order logic. The SNePS acting subsystem is integrated with the SNePS reasoning subsystem in such a way that: there are acts that affect what an agent believes; there are acts that specify knowledge-contingent acts and lack-of-knowledge acts; there are policies that serve as "daemons," triggering acts when certain propositions are believed or wondered about. The GLAIR agent architecture supports metacognition by specifying a location for the source of self-awareness and of a sense of situatedness in the world. Several SNePS-based agents have taken advantage of these facilities to engage in self-awareness and metacognition.

This paper presents a Prolog interface to the MiniSat satisfiability solver. Logic program- ming with satisfiability combines the strengths of the two paradigms: logic programming for encoding search problems into satisfiability on the one hand and efficient SAT solving on the other. This synergy between these two exposes a programming paradigm which we propose here as a logic programming pearl. To illustrate logic programming with SAT solving we give an example Prolog program which solves instances of Partial MAXSAT.

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.

We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted to those states that are reachable from the initial state. We demonstrate the usefulness of the above techniques for solving FOMDPs with a system, referred to as FluCaP (formerly, FCPlanner), that entered the probabilistic track of the 2004 International Planning Competition (IPC'2004) and demonstrated an advantage over other planners on the problems represented in first-order terms.