\documentclass[12pt]{slides}\usepackage{color}% usage:  \textcolor{cyan}{ Reasoning about action}% colors include cyan, red, green, yellow (pale) magenta% for 3400 display, compile on Powerbook 3400\setlength{\textwidth}{8in}\setlength{\textheight}{5in}% configs on Oztex, select A4 landscape\begin{document}\begin{slide}\begin{center}        \textcolor{red}{FORMAL REASONING GROUP}\\\vspace{0.3in}\textcolor{blue}{http://www-formal.stanford.edu/}\\John McCarthy (logical AI +)\\ Carolyn Talcott (math of  programs)\\ Tom Costello (logical AI +)\\ %Josefina Sierra (declarative formalization of heuristics)\\ Sa\v{s}a Buva\v{c} (formal theories of context) (finishing)\\ Eyal Amir( object oriented logic)\\Aarati Parmar (logic of action and knowledge)\\AFOSR, DARPA HPKB\end{center}\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}\begin{center}        ROADS TO HUMAN LEVEL AI? \end{center}biological---imitate human, e.g. neural nets, should work eventually\textcolor{red}{ engineering---solve problems the world presents},presently ahead\hspace{1.0in} direct programming, e.g. genetic algorithms, presently ahead\hspace{1.0in} \textcolor{red}{ use logic}, loftier objectiveThe logic approach is the most awkward---except for all theothers that have been tried.  \vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}{}  \begin{center}    \textcolor{red}{Logic in AI}\end{center}Features of the logic approach to AI---starting in 1958.\begin{itemize}\item Represent information by sentences in a logical language,  e.g. first order logic, second order logic, modal logic.\item Auxiliary information in tables, programs, states, etc. is  described by logical sentences.\item Inference is logical inference---deduction supplemented by some  form of nonmonotonic inference---1980.\item Action takes place when the system infers that it should do the  action.\item Observation of the environment results in sentences in memory.\end{itemize}\vfill\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{Topics, methods and problems of logical AI}  \end{center}  \begin{itemize}  \item deduction, nonmonotonic reasoning, theories of action,    problem solving,      reifying concepts, reifying contexts, approximate objects,    \textcolor{red}{elaboration tolerance}		\item \textcolor{red}{Elaboration tolerance (educate without brain surgery)}  \end{itemize}\vfill\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{ELABORATION TOLERANCE}  \end{center}\begin{quotation}\textbf{Three missionaries and three cannibals come to a river and find a boat that holds two.  If the cannibals ever outnumber the missionaries on either bank, the missionaries will be eaten.}\textbf{How shall they cross?}\end{quotation}\begin{displaymath}  \begin{array}[l]{l}  331  \rightarrow 310 \rightarrow 321 \rightarrow 300  \rightarrow 311 \rightarrow 110 \rightarrow 221 \rightarrow \\  020 \rightarrow 031 \rightarrow 010 \rightarrow 021 \rightarrow 000.\end{array}\end{displaymath}That's the solution.  What more is there to say?\vfill\end{slide}{}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{ENGLISH LANGUAGE ELABORATIONS (1)}  \end{center}  \begin{itemize}  \item The boat is a rowboat.  \item The missionaries and cannibals have hats,  all different.  \item Four missionaries and four cannibals    \end{itemize}    \end{slide}    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    \begin{slide}	  \begin{itemize}  \item There is an oar on each bank.  One person can cross in the    boat with just one oar, but two oars are needed if the boat is to    carry two people.  \item The boat leaks and must be bailed concurrently with rowing.  \item The boat may suffer damage and have to be taken back to the    left bank for repair.  \end{itemize}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{ENGLISH LANGUAGE ELABORATIONS (2)}  \end{center}  \begin{itemize}  \item There is a bridge.  \item There is an island.  \item Only one missionary and one cannibal can row.  \item The missionaries can't row.  \item If the biggest cannibal is isolated with the smallest  missionary, the latter will be eaten.\item The biggest cannibal cannot fit in the boat with another    person.  \end{itemize}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{ENGLISH LANGUAGE ELABORATIONS (3)}  \end{center}  \begin{itemize}  \item One of the missionaries is Jesus Christ.  Four can cross.    Here we are using cultural literacy.  However, a human will not    have had to have read Mark 6:\thinspace 48--49 to have heard of    Jesus walking on water.  \item Three missionaries alone with a cannibal can convert him into a  missionary.\item The probability is 1/10 that a cannibal alone in a boat will    steal it.  \item There are two (or $N$) sets of missionaries and  cannibals too far apart along the river to interact.  \end{itemize}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{KINDS OF ELABORATION (1)}  \end{center}  \begin{itemize}  \item irrelevant actors, actions and objects  \item adding preconditions, actions and objects  \item changing a parameter  \item making an entity situation dependent  \item specialization  \item generalization    \end{itemize}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{KINDS OF ELABORATION (2)}  \end{center}  \begin{itemize}  \item going into detail  \item missionaries and cannibals as actors  \item simple parallel actions  \item full concurrency  \item events other than actions  \item comparing different situations  \end{itemize}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{AD HOC AMAREL AXIOMS FOR BASIC MCP (1)}  \end{center}\begin{displaymath}  \label{3tup}  \begin{array}{l}States = Z4 \times Z4 \times Z2 \\\quad \\(\forall state)(Ok(state) \equiv \\\quad\quad  Ok1(P1(state),P2(state))\\ \land Ok1(3- P1(state),3-P2(state))) \\   \end{array}\end{displaymath}\begin{displaymath}  \begin{array}{l}(\forall m\ c)(Ok1(m,c) \equiv m \in Z4 \land c \in Z4\\ \land (m = 0 \lor m \ge c)) \\\quad \\Moves = \{(1,0),(2,0),(0,1),(0,2),(1,1)\} \\  \end{array}\end{displaymath}\begin{displaymath}  \begin{array}{l}(\forall move\ state)\quad\\(Result(move,state) =\\ Mkstate(P1(state) - (2P3(state) - 1)P1(move), \\                             P2(state) - (2P3(state)-1)P2(move), \\                             1 - P3(state))) \\  \end{array}\end{displaymath}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{AD HOC AMAREL AXIOMS FOR BASIC MCP (2)}  \end{center}\begin{displaymath}  \label{step}  \begin{array}[l]{l}(\forall s1\ s2)(  Step(s1,s2) \equiv \\            (\exists move)(s2 = Result(move,s1) \land Ok(s2)))          \end{array}\end{displaymath}\begin{displaymath}  \label{attainable1}  Attainable1 = Transitive\mbox{-}closure(Step)\end{displaymath}\begin{displaymath}  \label{attainable}  Attainable(s) \equiv s = (3,3,1) \lor Attainable1((3,3,1),s)\end{displaymath}From these we can prove\begin{displaymath}  \label{goal}  attainable((0,0,0)).\end{displaymath}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{SIMPLE SITUATION CALCULUS MCP (1)}  \end{center}\begin{equation}\label{movegroup}  \begin{array}[l]{l}\lnot Ab(Aspect1(group,b1,b2,s))\rightarrow \\Value(Inhabitants(b1),Result(Cross(group,b1,b2),s))\\\quad = Value(Inhabitants(b1),s) \setminus group \\\land \\Value(Inhabitants(b2),Result(Cross(group,b1,b2),s)) \\\quad = Value(Inhabitants(b2),s) \cup group, \\  \end{array}\end{equation}where $\setminus$ denotes the difference of sets.\begin{displaymath}  \begin{array}[l]{l}  (\exists x \in group)(\lnot Holds(At(x,b1),s)) \\ \rightarrow Ab(Aspect1(group,b1,b2,s)).\end{array}\end{displaymath}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{SIMPLE SITUATION CALCULUS MCP (2)}  \end{center}\begin{equation}  \label{bad1}  \begin{array}[c]{l}  Holds(Bad(bank),s) \\  \equiv\\ 0 < \\ Card(\{x|x \in Missionaries \land   Holds(At(x, bank),s)\}) \\ < Card(\{x|x \in Cannibals \land Holds(At(x, bank),s)\})\end{array}\end{equation}%\begin{equation}  \label{bad2}  Holds(Bad,s) \equiv (\exists bank)Holds(Bad(bank),s).\end{equation}\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{SIMPLE SITUATION CALCULUS MCP (3)}  \end{center}\begin{equation}  \label{rowers}  \begin{array}[l]{l}  \lnot(\exists x)(x \in group  \land Rower(x))\\ \quad \rightarrowAb(Aspect1(group,b1,b2,s)).\end{array}\end{equation}The oar-on-each-bank elaboration is expressed by conjoining\begin{displaymath}  \begin{array}[l]{l}Card(group) >\\ \quad Card(\{x|Oar(x) \land Holds(In(x,Boat),s)\}) \\\quad\quad \rightarrow Ab(Aspect1(group,b1,b2,s))\end{array}\end{displaymath}%\vfill\end{slide}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\begin{slide}  \begin{center}    \textcolor{red}{CONCLUSION}  \end{center}\begin{itemize}	\item  Human level AI is hard. 	\item   Logical AI is progressing.	\item  Too many researchers have too limited objectives.	\item Machine learning has been fixated on classification via	unary predicates. 	\item Maybe you should find your own approach---in logic or 	elsewhere.  (This was said to students).\end{itemize}  \vfill\end{slide}\end{document}