Emad Saad

Extended Fuzzy Logic Programs with Fuzzy Answer Set Semantics

This paper extends fuzzy logic programs [12, 24] to allow the explicit representation of classical negation as well as non-monotonic negation, by introducing the notion of extended fuzzy logic programs. We present the fuzzy answer set semantics for the extended fuzzy logic programs, which is based on the classical answer set semantics of classical extended logic programs [7]. We show that the proposed semantics is a natural extension to the classical answer set semantics of classical extended logic programs [7]. Furthermore, we define fixpoint semantics for extended fuzzy logic programs with and without non-monotonic negation, and study their relationship to the fuzzy answer set semantics. In addition, we show that the fuzzy answer set semantics is reduced to the stable fuzzy model semantics for normal fuzzy logic programs introduced in [42]. The importance of that is computational methods developed for normal fuzzy logic programs can be applied to the extended fuzzy logic programs. Moreover, we show that extended fuzzy logic programs can be intuitively used for representing and reasoning about actions in fuzzy environment.

Aggregates in answer set optimization

Answer set optimization (ASO) is a flexible framework for qualitative optimization in answer set programming (ASP). The approach uses a generating program to construct the space of problem solutions, and a preference program to assess the quality of solutions. In this short paper we generalize the approach by introducing aggregates in preference programs. This allows the user to express preferences which are based on minimization or maximization of some numerical criteria. We introduce the new language of preference programs, define its semantics and give an example illustrating its use.

Probabilistic Planning with Imperfect Sensing Actions Using Hybrid Probabilistic Logic Programs

Effective planning in uncertain environment is important to agents and multi-agents systems. In this paper, we introduce a new logic based approach to probabilistic contingent planning (probabilistic planning with imperfect sensing actions), by relating probabilistic contingent planning to normal hybrid probabilistic logic programs with probabilistic answer set semantics [24]. We show that any probabilistic contingent planning problem can be encoded as a normal hybrid probabilistic logic program. We formally prove the correctness of our approach. Moreover, we show that the complexity of finding a probabilistic contingent plan in our approach is NP-complete. In addition, we show that any probabilistic contingent planning problem,

Probabilistic Reasoning by SAT Solvers

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Disjunctive fuzzy logic programs with fuzzy answer set semantics

, can be encoded as a classical normal logic program with answer set semantics, whose answer sets corresponds to valid trajectories in

Learning to act optimally in partially observable Markov decision processes using hybrid probabilistic logic programs

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Bridging the gap between reinforcement learning and knowledge representation: a logical off- and on-policy framework

. We show that probabilistic contingent planning problems can be encoded as SAT problems. We present a new high level probabilistic action description language that allows the representation of sensing actions with probabilistic outcomes.

Reinforcement Learning in Partially Observable Markov Decision Processes using Hybrid Probabilistic Logic Programs

In a series of papers we have shown that fundamental probabilistic reasoning problems can be encoded as hybrid probabilistic logic programs with probabilistic answer set semantics described in [24]. These probabilistic reasoning problems include, but not limited to, probabilistic planning [28], probabilistic planning with imperfect sensing actions [29], reinforcement learning [30], and Bayes reasoning [25]. Moreover, in [31] we also proved that stochastic satisfiability (SSAT) can be modularly encoded as hybrid probabilistic logic program with probabilistic answer set semantics, therefore, the applicability of SSAT to variety of fundamental probabilistic reasoning problems also carry over to hybrid probabilistic logic programs with probabilistic answer set semantics. The hybrid probabilistic logic programs encoding of these probabilistic reasoning problems is related to and can be translated into SAT, hence, state-of-the-art SAT solver can be used to solve these problems. This paper establishes the foundation of using SAT solvers for reasoning about variety of fundamental probabilistic reasoning problems. In this paper, we show that fundamental probabilistic reasoning problems that include probabilistic planning, probabilistic contingent planning, reinforcement learning, and Bayesian reasoning can be directly encoded as SAT formulae, hence state-of-the-art SAT solver can be used to solve these problems efficiently. We emphasize on SAT encoding for probabilistic planning and probabilistic contingent planning, as similar encoding carry over to reinforcement learning and Bayesian reasoning.

Reasoning about Actions in Fuzzy Environment

Reasoning under fuzzy uncertainty arises in many applications including planning and scheduling in fuzzy environments. In many real-world applications, it is necessary to define fuzzy uncertainty over qualitative uncertainty, where fuzzy values are assigned over the possible outcomes of qualitative uncertainty. However, current fuzzy logic programming frameworks support only reasoning under fuzzy uncertainty. Moreover, disjunctive logic programs, although used for reasoning under qualitative uncertainty it cannot be used for reasoning with fuzzy uncertainty. In this paper we combine extended and normal fuzzy logic programs [30, 23], for reasoning under fuzzy uncertainty, with disjunctive logic programs [7, 4], for reasoning under qualitative uncertainty, in a unified logic programming framework, namely extended and normal disjunctive fuzzy logic programs. This is to allow directly and intuitively to represent and reason in the presence of both fuzzy uncertainty and qualitative uncertainty. The syntax and semantics of extended and normal disjunctive fuzzy logic programs naturally extends and subsumes the syntax and semantics of extended and normal fuzzy logic programs [30, 23] and disjunctive logic programs [7, 4]. Moreover, we show that extended and normal disjunctive fuzzy logic programs can be intuitively used for representing and reasoning about scheduling with fuzzy preferences.

Logical Fuzzy Preferences

We present a probabilistic logic programming framework to reinforcement learning, by integrating reinforcement learning, in POMDP environments, with normal hybrid probabilistic logic programs with probabilistic answer set semantics, that is capable of representing domain-specific knowledge. We formally prove the correctness of our approach. We show that the complexity of finding a policy for a reinforcement learning problem in our approach is NP-complete. In addition, we show that any reinforcement learning problem can be encoded as a classical logic program with answer set semantics. We also show that a reinforcement learning problem can be encoded as a SAT problem. We present a new high level action description language that allows the factored representation of POMDP. Moreover, we modify the original model of POMDP so that it be able to distinguish between knowledge producing actions and actions that change the environment.